Mathematics at the University of Florida in Gainesville, the first 65 years

Author - Dr. Paul Ehrlich - Math Professor - University of Florida - Gainesville

In 1957, the Soviets launched the first satellite into outer space, called Sputnik. I was a young boy at the time, but had already started watching television news specials with my parents. I can recall a whole series of scary programs on how the Soviet system was primed to overtake us in all areas of production, and that the United States had to do something about our lagging scientific and engineering education. A few years later in January, 1961, John F. Kennedy was inaugurated as President and at the time he took office, it was estimated that the Soviet growth rate was 6 percent to 8 percent per year, whereas the United States had a paltry growth rate by comparison of 2 percent to 3 percent. The Soviet Premier, Nikita Krushchev, had boasted that

``we will bury you--your grandchildren will live under

The Cold War was going full blast and I can recall that in this general time period, the newly created public television station in Schenectady, New York, started broadcasting a program on the Russian language every weekday at 6:30 a.m.. My parents purchased the book which went along with this program and for several months made my sister arise early with them and follow this program. For some reason, I was exempt from having to do this, but I did learn one or two Russian phrases. Thus Dean Simpson's study of Russian during his retirement fits very well into the cultural milieu of the times, as I remember them. On May 25, 1961, President Kennedy addressed a joint session of Congress in a nationally televised speech and among the things he said was

``I believe this nation should commit itself to achieving the goal before the
decade is out, of landing a man on the moon and returning him safely
to earth.''

In this time period, then, there was a dramatic increase in interest in and support for building the scientific infrastructure, including educational, in the United States. Mrs. Nancy Moore, who was studying in the graduate education curriculum at the time, recalls this period at the University of Florida as follows in an e-mail note of June 28, 1994:

``I can't help but point out that until about 1959 +, the federal government
didn't get actively involved with the school curriculum.  Then it was because
of Sputnik being shot into space by the Russians in 1957.  The government felt
that the US was behind in the space race.  That was bad, because that
meant that Russia might have new weapons to attack us from space.

I remember being enrolled in an education course in the 60's in
which the constitutional basis of the federal government getting
involved in education was discussed.  There was no constitutional
right for the federal government to get involved in education directly
(that was left to the individual states), so the `powers that be' saw
that ... they could get involved under the guise of needing to
defend the country.  Of course, what started out as direct aid to the
science curriculum (and the accompanying federal control) soon
expanded to social sciences etc. (and the accompanying federal control
that followed with the money).

I remember being in an education course in 1961 when the class was divided
into 2 groups.  One side had to argue in behalf of federal aid to education
and the other half had to argue against it.  That was a very controversial
subject then. (Money yes, but control no).''

I also recall that when I was first at the University of Missouri, the long time faculty members told me how Professor Blumenthal, their leading researcher, had been opposed to getting outside grant money when this issue first arose.

Marsden has the following comments on this particular time period, [1, pp. 393--394]. President Harry Truman's Commission on Education, appointed in 1946, which filed its report in 1947

`` ... was a prophetic voice announcing the advent of an era in
which the federal government would be a major force in making the
educational wilderness bloom through technique.  During the war the
universities had made an important contribution to national
defense. Perhaps the most telling sign of the times was that the most
momentous development during Robert Hutchins's tenure at the University
of Chicago was not anything having to do with the discussion of the
humanities or natural law; it was that in 1942, under the Amos Alonzo
Stagg football field, scientists at the university split the atom.
That secret work was the iceberg of which many other university
government contracts were the tip. The attitudes that emanated from
such successful cooperation grew into a conviction among government
leaders that the universities should continue to play a vital role in
national defense during the Cold War era.  By 1960 federal
expenditures for university research had reached $760 million
($20 million each if distributed equally among thirty-eight top
schools). Moreover, the National Defense Education Act of 1958
declared that `the security of the Nation requires the fullest
development of mental resources and technical skills of its young 
men and women.'


`this requires programs that will give assurance 
that no student of ability will be denied an opportunity for higher education 
because of financial need.' ''

Another interesting statistic given in [1, p. 427] related to the government expansion and vast increases in two-year colleges, community colleges, and higher education outside the humanities since 1960 is that while in 1960, about 15 percent of college faculty taught at a liberal arts college, by 1980, the percentage had dropped to 8 percent.

At the University of Florida, J. Wayne Reitz was President of the University from 1955--1967. During the early years of the Reitz administration, the Medical Sciences Building, the Teaching Hospital and the Pharmacy were completed at the J. Hillis Miller Health Sciences Center. McCarthy Hall was opened as the new home for the College of Agriculture and in 1965, Little Hall, named for the first Dean of the University College, Winston W. Little was completed. Dr. Linton E. Grinter had been hired in August, 1952 to succeed Dean Thomas Simpson. Grinter was hired with the title Dean of Graduate School and Director of Research. He had been at the Illinois Institute of Technology as Vice President and Dean of the Graduate Division there. He was the author of textbooks on structural engineering and mechanics and would serve as Dean of the Graduate School until 1968. A young, aggressive law school professor, Robert Mautz, who would later be Chancellor of the entire Florida University system, was moving up in the hierarchy. By 1954--55, he had the title of Assistant Dean and Associate Professor of Law. In 1958, Mautz became Dean of Academic Affairs.

In the last chapter, we have seen that Kokomoor worked during the late forties to get the Ph.D. program approved and our first Ph.D. was awarded in 1950. It is interesting to read the following about the development of the American University in general in this same time frame in William Duren's recent article in [2]:

``In the years 1950--1971 this country initiated an enormous
expansion of graduate studies in all fields of arts and sciences, not
just mathematics, bringing in many regional universities that had
never given the Ph.D. before and enlarging the older established
ones. ....''

It seems apparent that when we survey the written records from the 1950's at the University of Florida, that production of Ph.D. and Masters students seems to have played the role that publishing plays in the academic totem pole during the 1980's and 1990's. We find Florida mathematics faculty like Russell Cowan, William Hutcherson, Herbert Meyer, C. Basel Smith, D. E. South serving as supervisors to approximately 10 masters students each during the 1950's and early 1960's. Edwin Hadlock and C. Basel Smith, were dissertation supervisor for approximately 10 Ph.D. students each during this same time period. We also find on consulting the Mathematical Reviews Author Index for 1940--1959, that the strongest dissertations would often result in a publication with the thesis advisor and student as co-authors. During the 1950's, we find publications by Cowan, Ellis, Hutcherson, Hadlock, Phipps, C. B. Smith in this Index, but still get the sense that with 5 course teaching loads, that publications did not seem to play the role that they came to play following the tighter job markets starting with the 1970's. Nancy Moore can recall that Dr. Kokomoor encouraged faculty participation in regional American Mathematical Society and Mathematical Association of American Meetings, and remembers her father preparing lectures for these events, but the emphasis to rush every latest little new idea into print seems to have been lacking. Joseph Glover has commented that probably the necessity for research grant renewal also had a lot to do with the increasing emphasis on numbers of publications during the 1960's and 1970's. Here is a University of Florida Press release found in the A. D. Wallace folder in the University Archives which speaks for itself about regional meetings and faculty participation:

``GAINESVILLE, March [ed., 1967] --- Dr.
A. D. Wallace, newly appointed chairman of the Department of
Mathematics at the University of Florida, will present one of two major
addresses at the Southeastern Section of the Mathematical Association
of America meeting Friday and Saturday (3/31--4/1) at Florida Presbyterian
College in St. Petersburg.

More than 450 mathematicians from the Southeast and Puerto Rico are expected
to attend. 
Dr. F. A. Ficken, professor of mathematics and chairman of the Department of
Mathematics at New York University, will give the second address.

During the two day meeting, 10 University of Florida faculty will present
papers.  They are: Dr. Lal M. Chawla, Dr. J. E. Maxfield, Dr.
R. G. Selfridge, Dr. E. H. Hadlock, Dr. Amin Muwafi, Dr. William
Gager, Dr. Robert G. Blake, Dr. C. B. Smith, Dr. Kermit Sigmon 
and Dr. Waldemar Olson.''

On our own campus, there seems to have been an effort to build up research in general during the early 1960's, augmenting earlier efforts to build in the the applied sciences and engineering starting in the 1950's. The Records of the University of Florida reveal the following about the establishment of the Graduate Research Professorships. Even in the early and mid 1950's, there had been Research Professorships in Engineering and at various Experiment Stations. To name just a few, Henry Brown in 1952 joined the faculty and had the title in the catalogue of Associate Research Professor of Engineering and Industrial Experiment Station. Eugene Bovee arrived on campus in 1955 and had the title, Associate Professor of Biology and Sanitary Science and Associate Research Professor in Civil Engineering. Dr. Raymond Crist, a gentlemen who lived just a few houses away from me and who died in the spring of 1994, had been appointed already in 1951 with the title of Research Professor of Geography.

But if we are looking for GRADUATE Research Professorships in Arts and Sciences, the first we find seem to be the following:

So the establishment of the first Graduate Research Professorships in Arts and Sciences would seem, then, to coincide with the national movement in the late 1950's and early 1960's to build up the educational infrastructure, motivated in good part by Cold War fears. Professor Zoran Pop-Stojanovic also recalls that Graduate Research Professor John Slater, Ph.D. Harvard, hired in 1963 as a Graduate Research Professor in Chemistry and Physics was influential in the development of scientific research on the campus in the 1960's and 70's. (Slater was a member of the National Academy of Sciences.) Professor Al Bednarek has recalled that Dean Grinter was very interested in building up the research climate on campus with the aid of the institution of Graduate Research Professorship. Originally, these professorships were only in the graduate school, not formally attached to the departments [although this would later be changed during the Deanship of Charles Sidman, first dean of CLAS]. When someone stepped down from one of these GRP's, the graduate research professorship would not necessarily remain in the department. Other faculty have recalled for me conversations with Grinter in which he expressed his interest in appointing a Graduate Research Professorship in Mathematics and asked about prominent figures in Southern mathematical circles who could be brought to Florida to play a decisive role in building up the mathematics department. It was in these conversations that people recall the name of Alexander Doniphan Wallace, long time chair at Tulane, coming to the fore.

But it is interesting that evidence emerged serendipitously that even as early as the late 1950's, the administration was trying to help build our departmental research program during the Kokomoor Chairmanship. While writing up some memories of the Illinois mathematics department for my mother, I was led to read Paul Halmos's delightful book [3] and found to my surprise on [3, p. 239] that Professor Halmos writes:

``I continued to spend my quarters out of residence at far away places
 ...  and I received nibbles (and sometimes offers) of jobs (often
chairmanships) from several parts of the country (Urbana,
Illinois --- Gainesville, Florida --- Pullman, Washington --- Iowa City, Iowa).
The period I am talking about is approximately the four year interval
between 1957 and 1961.''

Naturally, this raised in my mind the question as to whether Professor Halmos had been considered for the position of outside chairman when Kokomoor retired in 1960. By this time, I had already corresponded by e-mail with Professor Halmos about the University of Illinois, so I took the liberty of sending him an e-mail message asking if he could recall the nature of his negotiations with the University of Florida after 35 years. In response, Professor Halmos went digging through his files, and sent me the following letter on April 7, 1995:

``Dear Professor Ehrlich:

   This is all I could find in the file labeled ``Old job correspondence'' ---
 still in view of our recent reminiscences, it may interest you.

Best regards,
Paul Halmos''

So here is a copy of the letter that Professor Kokomoor sent Professor Halmos, over 35 years ago:

                        University of Florida

College of Arts and Sciences                          January 17, 1958
 Department of Mathematics
    Walker Hall

Professor Paul R. Halmos
Eckhart Hall
University of Chicago
Chicago 37, Illinois

Dear Professor Halmos:

   We have open for the next academic year a research professorship that will
presumably involve the teaching of one three-hour graduate class, conducting a
seminar for members of our staff, and working and advising with some of our
graduate students.  We are looking for a man who would provide a
general stimulus to our whole graduate program in mathematics.  The
salary would be from $11,000 to $13,000, according to the
qualifications of the person employed.  The position is intended to be one 
of permanent nature.

   Your name has been suggested.  I should like to hear from you as to whether
you might be available.  If you are interested and are planning to attend the
Cincinnati meeting, I should like to talk the matter over with you at your 
convenience on Thursday, January 30.  I'll be staying at the Sheraton-Gibson 

   Four other members of my staff will be there several days longer.
I'd be happy if you would talk to as many of them as possible, too.
Altogether, we should be able to give you a fairly good idea of the nature 
of this position.

   The four are:  Dr. Alton T. Butson, Dr. Jerry W. Gaddum, Professor Diran
Sarafyan, and Dr. Andrew Sobczyk.

   If you are available and do not intend to attend the Cincinnati meeting,
I'll give you any information you may desire by mail.

                                                    Sincerely yours,
                                                 F. W. Kokomoor, Head
                                                Department of Mathematics


This surprise offer from Professor Kokomoor drew the following response from Professor Halmos:

                                                          January 27, 1958

Professor F. Kokomoor
Department of Mathematics
University of Florida
Gainesville, Florida

Dear Professor Kokomoor:

Thank you for your letter of January 17.  The slight delay in my answer
is caused by the fact that the letter had to be forwarded to me; I am spending
the current academic year on sabbatical leave at the Institute for
Advanced Study.  The same reason forces my answer to your flattering
inquiry.  In view of my present leave I feel morally obligated to
return to Chicago for at least one year, so that in fairness to you my
answer had better be that I an NOT available next fall.

                                                      Sincerely yours,
                                                      Paul R. Halmos

Now at this time, we had a mathematics department faculty member, Professor Gaines Lang, who had been a teaching assistant at the University of Illinois when Paul Halmos was an undergraduate. Perhaps this had something to do with the choice of Halmos as a target for recruitment as a research professor. I sent Professor Halmos a follow-up e-mail message requesting permission to quote this correspondence and also asking about Gaines Lang. Halmos replied that

``Yes, Gaines Lang was my teacher and my friend---he is (was) a good

In an article in the Gainesville Sun on July 16, 1994, Professor Seymour Block, Professor Emeritus of Chemical Engineering, who came to the University in 1944, had the following comments on the development of engineering at the University:

``In the late 1950's, the race to the moon was just starting, and
along Florida's Space Coast, the heartbeat of high tech was pumping
industry dollars into the economy.  He said there was a serious
movement to uproot UF's engineering department and move it to a new
state school in Orlando, then called Florida Technological University,
and now known as the University of Central Florida. 
    At that time, UF's engineering facilities consisted of only one
building, one lab and an old Navy airplane hangar. Block worked on a
committee that came up with a simple plan to stop the move.

    `If we could get buildings built, they couldn't move it,'
Block said.

The plan was presented to engineering Dean Joseph Weil, who had plenty of friends in the Florida legislature, then still dominated by the Porkchoppers, those politicians from the Panhandle and North Florida who had the votes to control nearly any issue, despite being at population disadvantage with South Florida.

`He did his own politickin',' Block said of Weil.

While reapportionment eventually ended the regime of the Porkchoppers, Weil moved in time to get the construction money and firmly anchor the engineering college at UF.

Block had also been active in the American Association of University Professors, both on campus, statewide, and nationally. In the early 1960's, when Gov. Farris Bryant came to town, the organization hosted a dinner for Bryant, where Bryant dropped an invitation to Block

`to come and visit me.'

Well, the next year, when Bryant vetoed a $700,000 appropriation for university faculty raises, Block decided to take up the governor's offer. The raises were an immediate issue, but Block also took along a plan proposed by the association that would expand and modernize the entire State University System with more money and more universities.

`He gave us a half-hour,' Block said of the governor. `We were in his office for
an hour and  half.'

Block didn't go alone; he invited two other faculty members so they could have a three-on-one advantage on the governor. The reasoning, he said, was that

`one could be thinking while the others were talking.'

 Block described Bryant as a `skin-flint conservative' who had a soft place in
his heart for education.  The group didn't get the governor to change
his mind on the raise, but a month after the meeting, Bryant put
together a task force to study higher education in the state.  The
group produced a study that mirrored the recommendations proposed by
Block and his colleagues.  Bryant then took the recommendation to a
special session and powered them through the Legislature.''

The University College was still going strong in the 1960's, which we should recall were turbulent years on college campuses, first, with Civil Rights issues causing dissension, followed a few years later by campus activities protesting the Vietnamese War. We happened to encounter an alumnus Daniel Harmeling, who graduated with the undergraduate degree in psychology in 1964, then took two years of graduate work in anthropology during 1964--1966. Thirty years or so after Professor Bradshaw remarked on the high dropout rates as we reported in Chapter 5, Harmeling recalls receiving the explicit impression after transferring in as a junior, but having to take some work in the Lower Division to remedy deficiencies in his course work in these basic requirements, that these courses were designed to weed the student body down to a decent size. He recalls being told,

``look to your right, look to your left, only one of you will
graduate. This is what statistics show.''

Nancy Moore recalled hearing the same phrase when she was a freshman in 1955--56. With this 2/3 attrition rate and the potentiality of being drafted to serve in the Vietnam War if one flunked out, apparently some students felt under some stress as Harmeling recalls. Indeed, his brother-in-law had precisely this experience happen to him, and has always remained bitter toward the University of Florida. In Chapter 8, we described resistance to female students entering the all male bastion of the College Inn. Harmeling recalls that in the early 1960's, the issue was the integration of this facility and recalls sustained picketing of the C. I. by students and faculty before it was integrated. Desegregation in Gainesville during the 1960's is also discussed in [4, p. 48]. Harmeling recalls that during the mid-60's, this flunk out policy came under increasing scrutiny; thus by the time Professor Lou Block was a student in the University College in 1965, he does not recall this vivid slogan of the 2/3 drop out rate being emphasized to the entering student body.

Now in our own Department, we would have had twenty years by 1960 of rule by a Chairman in his 60's, first, Dean Simpson in the 1940's followed by Professor Franklin Kokomoor in the 1950's. Theral Moore has recalled for me that as Kokomoor's retirement was nearing, no Chairman Search Committee was elected or appointed in the department, and that somehow the faculty expectation seemed to be that Professor Dudley South, who would have then been entering his 60's, would be appointed the next Chairman by the administration. Instead, the old guard of the department was about to experience an influx of new faculty who led a somewhat more lively life style, including an outside chairman Dr. John Maxfield, then in his early 30's.

Professor Robert Meacham, whom we encountered in Chapter 8, sent me the following recollections concerning relations between the administration and the Department on the selection of Kokomoor's successor in e-mail messages during August and September, 1995:

	``My recollections tell me that in the later fifties there were
15 to 20 full professors at the University of Florida.  When it came
time to replace Dr. Kokomoor, we discovered that Dean Linton Grinter
was playing his cards very close to his chest: indeed he controlled
the entire deck. Surprisingly he apparently never realized that we
had friends at other universities and from them we learned a good bit
about how Grinter was operating.

	First we learned that he had invited Professor Kleene from the University
of Wisconsin to apply, but Kleene said `NO'.  From John
Curtiss at the University of Miami, we learned that Curtiss was also invited
to apply, but Curtiss, who was a friend of several of us in the
department, also declined.  We got this information from Curtiss not
Professor Kenneth S. Miller, formerly from NYU or some other New York university,
came to make a talk or two, but I am not clear as to whether he was there because
of Grinter's invitation. 

	Why were the mathematicians annoyed at Grinter's end run past them?
They felt that as professionals they should be involved in the selection
of Kokomoor's successor.  It is certainly true that by pouring money
into the hiring of highly qualified mathematicians, the University of
Florida's academic and research status improved considerably.  Because
Grinter did not involve them in the search for a successor, a number of
those who were doing research and teaching upper level graduate courses
became unhappy with the climate.  When John Maxfield was appointed
chairman, he arrived to find an unhappy set of professors. 

	In August 1959 I was invited to come to St. Petersburg to participate
in a curriculum conference at this new college. [ed., Florida
Presbyterian College] Dean John M. Bevan asked me to set up the
mathematics program.  He had already invited me to be the founding
professor of mathematics, but I declined.  At the curriculum
conference I met the others who had signed on as founding faculty.
The program we set up was so exciting that we agreed in August 59 to join the
others a year later, when the founding freshmen class would arrive.

	Consequently the entire year 59--60 was my last year at the
University of Florida.  I was therefore not affected personally by
Grinter's go-it-alone approach to hiring a new mathematics chairman at
U.F. Because I had experienced the same sort of Deanish behavior
at Carnegie Tech, I was very glad that I had already signed on with
Florida Presbyterian College before this academic year 

Meacham recalled that over a several year period, Andrew Sobczyk and Alton Butson relocated to Miami University; Meacham recruited Dudley South down to Florida Presbyterian to handle the Statistics program; John T. Moore went to the University of Western Ontario; Russell Cowan went to Lamar University at Beaumont, Texas; C. B. Smith went to Trevecca Nazarene College in Nashville; and Cecil Phipps went to Tennessee Tech University in Cookeville.

The student newspaper, the Florida Alligator, from the fall of 1960, Professor John Maxfield's first semester as new outside chairman, gives a bit more vivid of a picture of the conditions Maxfield found when he arrived on the scene. A September issue of this paper reveals that enrollments were expected to set a new record; with one more week of late registration to go, 12,692 students had already enrolled. The University College, i.e., the Lower Division, which we have encountered in earlier chapters after its establishment in 1935, had an enrollment of 4,968 males and 2,178 females. In the Upper Divisional Instruction, the College of Arts and Sciences had enrolled 1,371 by this point in time, the College of Engineering had 1,041 enrolled, and the College of Education had 916 enrolled. There were two females registered in engineering and ``one lonely male registered in a school of 66 female nurses.'' On the same page of the Florida Alligator, it is reported that the Seventh Annual Scholarship Convocation was to be held with guest speaker Dr. George Wald from Harvard lecturing on ``The Origin of Life'', and also Dean Robert Mautz was scheduled to discuss ``the intellectual revolution on campus among the faculty and student body.''

A long article in the September 23, 1960 Florida Alligator was devoted to space needs on campus, with extensive quotations from Dean Mautz and Dean Ralph Page.

	``Overcrowded classes, a long brewing problem area, burst wide open
this week as classroom jamming reached unprecedented proportions.
	The critical conditions in jammed classrooms that prevailed as
doors opened Monday caused a great shift of students from room to room,
especially in Peabody Hall. Administrators were trying to re-allocate
the largest classes as best as they could.

	The direct cause of the overcrowded conditions was an enrollment
increase of 509 students.
	Dr. Maurice Boyd, head of the C-1 department, explained that
junior colleges are not relieving the situation at the UF as expected.
	`With 50 students in some C-1 sections, quality education and
discussion become next to impossible,' he said.

	Arts and Sciences, the hardest hit college, has an increased
enrollment of 12.1 per cent over last year.  Only two new teaching
positions have been added, and that was a result of what Arts and
Science Dean Ralph E. Page termed the `desperate situation that

	`What doesn't show up is the number of students from other
 colleges who take Arts and Sciences courses.'

Enrollment Up

	`We're dealing with really astronomical proportions,' he said, `when you
 realize that our student course enrollment figures this year
are 19,380 as compared with 18,355 of last year.'

	Building-wise, UF's most pressing need is a social science-humanities
classroom building and an architecture building, according to Dean

	`These were appropriated by the legislature, but the funds were never
released by the cabinet because of the big freeze in Florida the winter
of 1957--1958,' he said.

	The social science-humanities building will go south-southwest of the 
Administration Building if it is re-appropriated.''

So that is the genesis of Little Hall!

In the September 30, 1960 Florida Alligator, an article headlined ``Altered Schedules Eyed'', to cope with increased enrollments and classroom crowdings, reported that

	``Peabody, Anderson, and Walker Halls were visited by Dean Mautz
during the busy morning hours. `I saw for myself the crowded situation
in those three most packed buildings,' said Dean Mautz, `and I will
report on what I saw to University Vice-President Harry M. Philpot,
who is chairman of President Reitz's [ed., special]
committee. [ed., on crowded conditions]' ''

In these times, the Florida State Legislature met only every other year. Apparently, the support for education during the 1957 and 1959 terms had not been so munificent, as reflected in Mautz's comment above about appropriated funds being withheld as a result of a freeze affecting the citrus crop. In the October 4, 1960 Florida Alligator, an article headlined [Student Body President Robert] ``Park Protests Newsweek's Views'' gave Bob Park's objections to aspects of an article in the September 26, 1960 issue of Newsweek on the role of the Florida legislature in supporting higher education.

	``In a wire to Newsweek headquarters in New York City, Park
stated: `Florida is first in the Southeast in per capita income, but sixth
in expenditure in the Southeast for higher education.

	The University of Florida faculty is short 241 positions.  Professors'
salaries are shocking.  Buildings are overcrowded.  Alumni and students are
conducting a statewide campaign to focus attention on the critical
needs of universities of Florida for the 1961 legislature.'

Facts Show Lack

	Park's statements said the facts on the needs of higher education in
Florida `clarify the need for truly inventive and forceful action in
the Florida's university system.' Park also stated, `we are proud of
Florida's great and recent progress in higher education and are anxious
to keep this movement going forward.'

Truth Must Out

	Park told the Alligator, `the truth must be told to the people
before the 1961 legislature meets. The trend of whitewashing Florida's
higher education must be overcome,'

In reference to the content of the Newsweek article, Park said,

	`A good story on the [ed., new] University of South
Florida was soured by misrepresentation of the full picture.

	The legislature failed to provide sufficient funds for higher
education in 1957, and cut the budget recklessly in 1959.  Next
year is sink or swim for higher education in Florida.' he

The September 27, 1960 Florida Alligator carried an article about Dean of Arts and Sciences Ralph E. Page's guidelines for faculty promotion and salary increases. The overall evaluation was to be based on teaching quality (55 percent), research performance (30 percent), and service to the University (15 percent). A memo sent to department heads, according to the Florida Alligator, reveals a more detailed description of the criteria for the three areas of the academic trinity. In teaching, we find guidelines:

In the areas of research and service, we find

Service Significant

Of course, here at this point in time we were still a good decade away from the renovation of Walker Hall, remembered so well by Professor Kermit Sigmon among other faculty who have discussed the University of Florida in the 1960's and 1970's with me. This need for renovation is dramatically reflected by a series of articles in the Florida Alligator concerning fire safety in Walker, Peabody and Benton [ed., now the site of Grinter Hall] Buildings. On October 21, 1960, the Florida Alligator printed an interview with Chairman Maxfield titled ``Math Dept. Not Able to Match Other Schools'' and noted that ``The Alligator this week investigates conditions in the Math Dept. in the fifth of the series on overcrowded conditions.''

	``One wall of Maxfield's office is covered by a pink and black schedule
board, with the schedules, teaching load, and amount of training of his

	Yellow stripes across certain hours indicate course being taken by faculty
members or graduate assistants.

	`We have 38 full time faculty members,' said Maxfield.

	`We would have had 40 but two did not come here---one simply
didn't come, the other had to go elsewhere for more money.

	The resultant shortage means that every graduate student teaching
half-time must teach four courses yearly; every graduate student teaching
one-third time, must teach three courses.'

	At other schools, according to Maxfield, graduate assistants are ordinarily
required only to teach two courses yearly.

Unusual Situation

	`This is an unusual situation.' he emphasized. Interim teachers---those
working for advanced degrees---are a large portion of the Math department
faculty. `Every one of these teachers plans to get either a master's or a
Ph.D. degree,' says Maxfield.
  1. Facilities for teaching in the underwater atmosphere of Walker Building are as in other buildings---inadequate.
  2. The underwater look is due to the green skylights and stairways which angle up narrow dark hallways.
  3. The 17 graduate assistants are housed in a room on the third floor, set in an alcove which juts two feet left on one side then two on the other to give a jigsaw effect.
  4. There are five desks for these student-teachers.
  5. There are not even 17 drawers for the 17 students.
  6. Nor are there chairs for more than five people at once.
	`That's my favorite room.' says graduate assistant Arnold Inshel.
 [ed., actually Insel] `We graduate assistants get together
 there sometimes and discuss our mutual problems!'

	Classes in the Walker building feature 18 or 20 foot high ceilings and
blackboards set 30 inches off the floor. One desk is located in a small hallway
leading off the main hall into an office for two men.

Some Joke

Professor Heinryk Mince, [ed., actually Minc] who has this hall desk, says jokingly, `I talked to a student for half an hour yesterday before I found out that he just wanted to go by.' He went on to say that at his former school there was a mathematics library and a mathematics reading room in the main building. `There is nothing like that here.' Is the UF math department able to compete with the math departments of these other [ed., 21 Universities with which UF compares itself] universities? `No,' said Maxfield, ` Salaries are just not high enough, nor are conditions. Mathematics is a creative field, and new work is being done all the time,' he says. `We have several good people coming for next fall already.'

Main Problem

` Our main problem is to keep them and to build up our department to the point that we will be staffed by and producing outstanding men with advanced degrees.' ''

Earlier on October 14, 1960, the Florida Alligator had printed an article ``Dr. Reitz Asked by Bob Park For Fire Hazards, Safety Report'' in which the student body president Bob Park was urging President J. Wayne Reitz to look into campus fire hazards, following the issuance of a pamphlet by the U. F. Alumni Association on this issue. In this pamphlet, it is stated that 13 percent of UF's buildings are ramshackle wooden firetraps, and clogged stairwell conditions existed in Anderson, Peabody, Walker and Benton Halls during class breaks at peak class hours. In preparation for the Alligator Homecoming issue, Pat Tunstall, Gator Editorial Assistant wrapped up her series of articles on overcrowded conditions with the following dramatic prose on Friday, November 11, 1960:

``Thirteen Thousand Students Hit Hardest Ancient UF Class Halls Choked By Congestion at Peak Traffic Hours

A numbers game---trying to cope with seven stairways, seven doors, and hundreds of students---makes the internal triangle---Benton, Walker and Peabody halls---one of the most congested areas on campus. Every hour on the half-hour, students pour into and out of the doors of these three buildings and head across Union Drive. Traffic is at its peak in the morning hours during class changes, as big cars, small ones, motor scooters, bicycles and students converge on the narrow drive. Walker Building, with it's long marble stairway to the front door presents one peculiar problem. The internal stairway, which seems to penetrate through the heart of the building to the back door is choked up with students going both ways, on either side. The front door of Walker looks into a steep worn marble stairway, with abrupt turns and small landings. During the hours 7:40 to 1:40 at class changes, students and faculty are forced to shove themselves through the throng. `Actually, you don't have to move very much,' said one student on the way up. `If you just stand still, the crowd almost forces you up.'

Everybody Pushes

Students do not use one side for up and one for down. Both wells are filled with book laden bodies pushing to the left, right and in the middle. `Walking up sideways is the only way to go in Walker,' said a girl. `You can't slide through if you're going head-on.' Separated from Walker by a narrow alley is Benton Hall. The two doors of Benton lead to Union Drive and Murphree Way. On the Murphree side is a small hall, leading to another steep stairway, though not so narrow as in Walker.

Railing Weak

The stairway railing threatens to give way at the top landing if a student should lean on it. `Remember last year when the plaster fell on the the building. That was really something.' ....''

On the other hand, in this same issue, an interview with Dean of Academic Affairs Mautz is headlined ``No Single Spark is Cause For Dramatic UF Change.'' Mautz writes

	``The Faculty furnishes the inspiration and leadership for
intellectual activities, and defines the goals toward which all
strive.  This they have done with marked success. Objective
measurements of intellectual leadership are difficult. Let me provide a few.

	The faculty continues to attract a substantial amount of research
and grant money.  In 1959--60, the University had in process
$3,000,000 worth of projects financed by other than State appropriations.
Articles in scholarly publications are increasing in number.

	As a member of the Personnel Board, I see letters from persons at major
intellectual centers of the world, which attest to the high quality of these
articles.  Other marks of recognition of the merit of their work increasingly
comes to my attention.  Books, displays, and art shows attract
critical acclaim.''

Earlier, in an October 28, 1960 interview with Board of Control Chairman J. J. Daniel, it was reported that the University of Florida Foundation had received an increased number of gifts and grants as a result of the ``Sputnik hysteria.'' Mrs. Nancy Hadlock Moore had the following comments on these articles based on her own recollections of this time period:

	``Walker Hall remained in that same fire trap status until it was
renovated in the early 1970's. [Professor] Theral [Moore] should remember 
dates. And others would!

	Benton Hall was so bad, it was recommended that only graduate classes
were to be scheduled on the top floor. Was it because they wanted
fewer people to be buried in the rubble in case of collapse? Or that and
did they think the added weight of people at the top would make the
building more apt to crumble.''

In an e-mail message of June 14, 1995, Professor Kermit Sigmon was kind enough to share with us his recollections of these times:


I didn't arrive in Gainesville until August 1963, so I can only
comment on things that I recall from that date forward.
Here are a few comments:

---  You mention the ``renovation of Little Hall'' at one point.
     I suppose you mean ``Walker Hall''. [ed., yes, I made a slip up
     here in the draft of this portion of the chapter I circulated
     to the faculty by e-mail.]  This renovation occured
     during AY 1972-73.  The department moved to Building E in the
     summer of 72 and back into the extensively renovated Walker Hall
     in the summer of 73.  Building E was the ``barracks'' (actually  in
	 the shape of the letter E!) sitting just north of the
     current Little Hall, where there is now a parking lot.
     Building E burned down (accidentally???) within a couple of years of 1973.

---  During my 3 years as a doctoral graduate student (63-66), I was
     actually an ``Interim Instructor'', a line-item position, as
     mentioned by Maxfield (rather than a TA).

---  The graduate student ``alcove'' mentioned was actually a rather large
     room on the west end of the 3rd floor containing desks packed in.
     In the prerenovated Walker Hall it sat where the current offices
     of Rao, Block, Cenzer, Pop-Stojanovic, Bao, and men's toilet now sit.
     My desk was in this room during my first year here.

---  Note that then grad student Arnold Insel (not Inshel), quoted in
     the Alligator  article, is one of the authors of the 
     Friedberg/Insel/Spence Linear Algebra text used by some in MAS 4105.

---  The prerenovation classrooms in Walker were unairconditioned with
     huge, noisy exhaust fans.

---  Benton Hall was condemned sometime in the 60s because of danger of
     collapsing.  The department once held its regular colloquium in
     a Benton auditorium.  Grinter Hall replaced it, of course.

---  When Walker Hall was renovated, those slate classroom
     blackboards mentioned in the 1960 article about the Walker Hall
     classrooms were preserved and used for the blackboards in the current 
     faculty offices in Walker Hall.

These are a few thoughts spurred by the article.


Professor Sigmon also recalled very vividly to me how the new outside Chairman Maxfield, then in his mid-thirties, had a commanding presence when Kermit was a graduate student; for Maxfield stood around 6' 6'' and had a fine handle bar mustache. He also brought to Gainesville a collection of vintage Rolls Royces and a stretched Checker limousine. (Kermit recalls driving to an American Mathematical Society Meeting in Houston in the Checker limousine, with Dr. Maxfield and a group of graduate students during his time in graduate school here.)

The ever helpful 1955 American Men of Science reveals that Dr. John Edward Maxfield was born on March 17, 1927 and had married his wife Margaret Waugh Maxfield in 1948. He received his B.S. in 1947 from M.I.T., the M.S. from Wisconsin in 1949, and the Ph.D. in mathematics from the University of Oregon in 1951. He had served as an Instructor in Mathematics at the University of Oregon during 1950--1951, then gone to the Naval Ordnance Test Station at China Lake, California in 1951. He listed his research interest as being in algebra and described his specialized research interests more specifically as ``number theory; analog and digital computing techniques.''

The 1992--1993 American Men and Women of Science enables us to follow the trail further along. Here we learn that Dr. Maxfield had been at the Naval Ordnance Test Station from 1951--1960, and during 1958--1960 had served as the Head of the Mathematics Division there. He then served as Professor and Head of the Department of Mathematics at Florida from 1960--1967, as Professor and Head at Kansas State University from 1967--1981, and in 1981 became the Dean of the Graduate School and University Research at Louisiana Tech University in Ruston, Louisiana. This latter volume also shows ``numerical analysis'' as a third research interest of Dean Maxfield.

The card catalogue reveals three books with John Maxfield as co-author in the University of Florida Libraries. The first, with Ralph Selfridge, is titled A table of incomplete elliptic integrals of the third kind, and was released within the Department of Defense as NAVORD report 5643, NOTS 1870, then published by Dover Publications in 1958. Today this work is housed in the Reserve Section in Marston Science Library. The Forward for this book provides us with the following information as to its purpose [5, p. iii]:

	``The tables included in this book were computed to solve a specific
problem.  It was found that the surface area of certain geometrical bodies
could be expressed only in terms of the incomplete elliptic integral of the
third and lower kinds.  A search of the literature was made, which determined
that complete values for the integral of the third kind were not available,
and it was therefore decided to compute such a table.

	This table will be of greatest use to physicists, engineers, and applied
mathematicians who work in the fields of fluid dynamics, heat flow, and related
topics.  The integral appears in the solution of problems dealing with
the motion of the spherical pendulum and related mechanisms, in
problems of magnetic potentials due to circular current or of the
gravitational potential of a uniform circular disk, and in certain kinds of
seismological work.
The actual computation of this table was performed in 1956 and early 1957 on an IBM Type 704 Calculator; the greatest difficulty was encountered not in constructing the table but in obtaining satisfactory checking.'' [ed., Professor Ralph Selfridge has informed me that this IBM machine was an early programmable computer with plug board wires.]

On [5, p. xi - xii], a bit more detail is given:

	``The tables were produced ... using a simple Simpson's Rule method of
integration. The results of integration were stored for each .01 radian, and
printed out in groups of ten lines at a time.  In order to compensate
for accumulated roundoff in the angle, every .1 radian was fed in
from a separate list, adjusting the mesh size for one integration, so
that at no point is the angle in error by more than 10^{-7}.

    The method of printing is naturally of concern, since a large
amount of error can occur here. Printing was handled by the computer
using a method known as echo-checking.  With this process, the type
wheels are set as ordered, and then an independent pulse is returned
to the computer, indicating what symbol has been printed.  A
comparison of the return, or echo, with the initial command ensures that
what was printed is what was desired.  After being printed by the computer,
the tabulation was reproduced by the photolithographic process, so that there
should be no variation between the initial printing and the final

    There still remained the problem of checking the computation.  This was
handled in the following way: Computation proceeded by Simpson's Rule
with a mesh size of about .0025 until phi = 1.57. At this point
the mesh size was changed so that the next point was computed with
phi = pi/2, yielding all the complete integrals.  An entirely different
method was then used for obtaining the complete integral, and this has
been printed as the last line of each group in the table.
Comparison between these lines gives a very excellent indication of the upper
limit of the error. ...''

The second work [6], Contemporary mathematics for general education: algebra, was published with Margaret Maxfield and S. Gould Sadler, and was the text for the Lower Division C-42 General Mathematics course which the reader may recall being an aspect of life at the University of Florida discussed in earlier chapters; the Chairman of Mathematics served not only as Chairman of Mathematics in the College of Arts and Sciences, but also as Head of the C-42 Course: Contemporary Mathematics in the Lower Division. By this point in time, materials written by Professor Kokomoor for this course after the University College came into existence in 1935 and which served as the basis for Kokomoor's text book published in 1942, would have been used for 25 years.

The third book [7] in our library with John Maxfield as co-author is an undergraduate text book on abstract algebra published with Margaret Maxfield, titled Abstract algebra and solution by radicals, W. B. Saunders Company, 1971. This work is deliberately written to be read by the student encountering abstract algebra for the first time, as contrasted, say, with a well known work the author wrestled with in college, I. Herstein's Abstract Algebra. I cannot resist quoting just two lines of [7, page viii] which reveal the delightfully written style of this book, at least from the instructor's viewpoint:

	``The Appendices can be used to further your interest along several
different lines barely suggested in the text.  They offer an opportunity
for outside work to bolster a sagging grade. ...''

Professor Al Bednarek has recalled that Dean Linton Grinter was very much interested in building up the applied research on campus. Thus Maxfield, with his background in computation and scientific management at the China Lake Naval Ordnance Station, as well as his training in pure mathematics (both Margaret and John Maxfield had taken Ph.D.'s in number theory at the University of Oregon with supervisor Professor Ivan Niven), fit well into the administration's plans for campus development.

The Professor Henryk Minc, mentioned above in the Florida Alligator article, was hired in 1960 and specialized in fluid dynamics. Also Dr. Maxfield hired several people who had been with him at the China Lake Naval Ordnance Station, including Professor Ralph Selfridge, currently in the Computer Science Department at the University of Florida. As we have already noted, in these far off days of 1959--1960, it was not felt necessary to spread a thin veneer of democracy over all proceedings.

Professor Theral Moore still recalls very vividly how the choice of Kokomoor's successor was made. There was no departmental committee involved in the selection process. After the candidates selected by Linton Grinter had made campus visits, Dean Ralph Page, whom I quoted above in the Florida Alligator articles, came to meet with the Mathematics Department faculty and announced in resonant, orotund tones, that

``the choice of new Chairman was his to make, not the Departments,''
and that it would be Dr. John Maxfield.

At the Annual Winter Meeting of the American Mathematical Society held in Orlando during January, 1996, Dean John Maxfield kindly granted me an hours interview and thus I had the opportunity to speak with him myself about how he came to Florida. I asked him how a specialist in number theory came to be at China Lake instead of taking an academic position. Maxfield replied that the work during the summer while he was a graduate student seemed so interesting to him that when permanent employment was offered upon his receipt of the Ph.D., he accepted the position. He was the first mathematician in a group at the China Lake Naval Ordnance Test Station that designed the sidewinder missile.

Maxfield confirmed that all the impressions I had received that Linton Grinter wished to change the mathematics at the University of Florida toward a more applied direction were indeed correct. One of the consultants at China Lake, Professor William M. Whyburn of the University of North Carolina at Chapel Hill, was a friend of Grinter. Whyburn had come to know Maxfield when Maxfield was head of the mathematics group at China Lake. By 1960, the work in mathematics at China Lake was becoming less attractive than it had been earlier, so Maxfield encouraged Ralph Selfridge (as well as Wayman Strother, whom we will encounter later in this chapter) to leave China Lake for academia, as well as leaving himself.

Over 50 years after Professor Karl Schmidt was offering astronomy as well as mathematics during 1905--1908, during the Maxfield chairmanship, mathematics was STILL offering Astronomy. The 1962--63 Catalogue and Record contains the following entries:

                               `` Astronomy

                      INSTRUCTIONAL STAFF  1961--1662

    Maxfield, J.E., Head; Awtrey, R. A.; Cowan, R. W.; 
    Morse, W. P.; Selfridge, R. G.

    ATY 141 -- DESCRIPTIVE GEOMETRY. 3 credits
      Not open to students who have had any other course in astronomy.  An 
      elementary survey of the astronomical universe. Primarily intended as 
     an elective for those not majoring in a physical science or mathematics.

    ATY 305 -- CELESTIAL NAVIGATION. 3 credits
    Prerequisite: MS 205 or its equivalent.  Determination of position at 
    sea and in air, guidance of marine vessels and aircraft.  Topics studied 
    include charts, the compass, dead reckoning, piloting, nautical astronomy,
    navigational instruments, the navigator's work at sea.

    ATY 306 -- CELESTIAL NAVIGATION. 3 credits
    Prequisite: ATY 305. The second half of the course ATY 305-306.

    ATY 316 -- GENERAL ASTRONOMY. 3 credits
    Prerequisite: MS 205 or its equivalent.  Survey of the solar system.
    The earth, sun, moon, planets, comets, asteroids, and meteors.
    Recommended for majors in a physical science or mathematics, or those who 
    have had some previous work or experience in astronomy.

    Prerequisite: ATY 316. The stellar system. Distances, masses,
    luminosities of the stars. Eclipsing and spectroscopic binary stars.
    Interstellar matter and the galaxies.  An introduction to astrophysics.''  

Now that we are studying the Maxfield Chairmanship, fortunately we have entered a time period of which faculty members Al Bednarek, Charles Nelson, Zoran Pop-Stojanovic, and Kermit Sigmon as well as Theral Moore, all had graphic memories to share with me. Almost thirty years after the fact, Charles Nelson still recalled vividly from his first semester in Gainesville the faculty and teaching assistant meeting that was held on a Sunday afternoon in a room in the Architecture Building, just before the beginning of the fall semester.

Professor Maxfield would have received the student enrollment figures that previous Friday and Saturday, and by Sunday afternoon, Maxfield would have worked out the teaching schedule. At this Sunday afternoon meeting, Maxfield handed every faculty member, interim instructor, and teaching assistant a 3'' x 5'' index card containing their teaching assignment for the semester. In those days, Nelson recalled, one did not complain to the Chair or Associate Chair about teaching assignments, but just do informal swaps.

Also, since everybody was assembled together in one place, the Seminar Schedule for the semester would also be drawn up at this same time. Nelson recalls that when he arrived in 1966, Maxfield gave him the choice of sharing an office which was airconditioned, or having an office to himself which was not airconditioned. Chuck chose the former option, so found himself for a time in Little Hall 440 with office mate Jorge Martinez. (After Professor Ernie Shult went to Kansas State several years after Maxfield went there as new outside chairman in 1967, Florida Chairman Al Bednarek asked Nelson if he would like to move into Walker Hall, so Nelson found himself in Walker 107, now vacated by Shult's departure for Kansas.)

During the Maxfield Chairmanship, part of Nelson's teaching assignment was the comprehensive C-42 course in the University College. Weekly quizzes were given, and Nelson liked to hand in a fill-in-the-blanks quiz of 10 questions to be typed up for this purpose. One day Nelson found Chairman Maxfield holding the typed quiz when Nelson came for it; Maxfield informed Nelson that from now on, he was to give a multiple choice quiz rather than a fill-in-the-blanks quiz. Several faculty had recollections of Maxfield somehow obtaining room airconditioners for many of the Walker Hall offices.

Of course, everyone remembered those Rolls Royces! Kermit Sigmon recalled a well known quotation stemming from the time that Maxfield left Florida for Kansas State:

``it was a pull, and not a push.''

On February 21, 1994, I sent Dean Maxfield a letter inquiring about some of these issues. To my pleasant surprise, Dr. Maxfield telephoned me on March 16, 1994 and answered many of my questions, and later, sent me during the fall of 1995, a packet of newspaper clippings from his Gainesville years, which further helped fill in some details. Maxfield told me that at the China Lake Naval Ordnance Station, he had become the Head of Computing as well as Head of Mathematics, in charge of their computer center. At Florida, Maxfield was not only as Chair of Mathematics and Astronomy from 1960--1967, but also Director of the Computing Center from 1961--1964. One of the newspaper clippings shows Maxfield at a computing center dedication and reads

                    ``Computing  center dedication

From left, UF President J. Wayne Reitz, Floyd B. Bowen of Lakeland, member 
of Florida State Chamber of Commerce, and Dr. John E. Maxfield,
director of UF's Computing Center, observe the new IBM 709, which is
capable of computations 50 times faster that the one previously used
by the UF.''

After I showed this material to Kermit Sigmon, he recalled taking Numerical Analysis during 1963--64 with Professor Ralph Selfridge, whom Maxfield had brought to Florida with the rank of Associate Professor during the 1961--1962 academic year. (During 1959--61, Selfridge was involved with starting up the computing facility at the Miami University of Oxford, Ohio during the Strother chairmanship of that Mathematics Department.) By 1966, Selfridge had been promoted to Professor and was also Director of the Computing Center. Sigmon recalls having to bicycle from Walker Hall all the way to what is now called the Wallace Building in the agricultural complex near Fifield Hall on the other side of Lake Alice in order to have the Fortran programs which were assigned in this Numerical Analysis course run on a main-frame computer.

Maxfield told me that the recollections of several faculty members about the installation of air conditioners in Walker Hall were indeed correct. In Chapter~8 we have learned that when the engineering faculty left Walker Hall, they took their own air conditioning installations with them to Weil Hall, and thus during the Kokomoor chairmanship, Walker Hall was not airconditioned. Since the homes were also usually not air conditioned in Gainesville in those days, Maxfield recalled for me

	``Secretaries or machinery could have airconditioning, but not
faculty, using state money that is.  It was clear that in order to get any kind
of research going, one needed airconditioning.  State money would pay for wiring
the rooms for airconditioning, thus I bought either 9 or 13 room airconditioners
at an auction, and donated those to the department when I left for Kansas

(In roughly this same time frame, Jed Keesling happened to be also living in Gainesville and attending junior high school. He recalled for me how during that time, only the main roads were paved, but not the streets in the subdivisions. Thus with the lack of airconditioning, Jed recalls his mother's battles with the dust stirred up by local traffic that would accumulate inside the houses especially during the hot summer months.)

Maxfield also recalled for me that the Statistical Laboratory, housed in one of those temporary buildings by McCarthy Hall and which was discussed in Chapter~8, was being phased out early in his chairmanship as a Department of Statistics was being established in the Agricultural College.

Here is what the October 30, 1963 issue of the Florida Alligator had to say about the Rolls Royces:


                    Prof Repairs Rolls Royces

	Owning a Rolls Royce is perhaps not such a novelty as it once was,
but Dr. John Edward Maxfield has owned as many as 10 at one
time. Maxfield, 35, is head professor of mathematics at the UF.

	Evenings and weekends Maxfield surrounds himself with carburators,
generators, radiators and other assorted automobile parts.  With these
within easy reach of his 6 feet 2 frame, he takes leave from the academic
world and loses himself in his hobby.

	Maxfield buys only Rolls Royces in need of repair.

     	`After all, repairing the cars is my hobby. I really enjoy working with 
     such fine machinery,' Maxfield said.

	After Maxfield puts the cars in perfect running order, he sells them. 

     	`Sometimes people just see one and want to buy it.'

	To keep the cars in good running order, Maxfield and his wife, Margaret, 
drive their 6,000 pound machines everywhere they go.

     	`We often take them places most people wouldn't drive a jeep. They handle
     wonderfully,' he added.

	Regular gasoline is used in the cars.  They average eight to 14 miles per 

	Most of the cars have `Q' license plates, signifying they are at least 20 
years old.

	Maxfield does almost all of his own repair work except for

	The chassis parts come from the Rolls manufacturer, but the body parts must be 
made as he needs them.  Maxfield said that body work is hardest.

     	`I guess I just enjoy the mechanical work more,' Maxfield said.

	Maxfield's wife approves of his pastime.  He said she has acquired quite a 
bit of knowledge about the Rolls Royce and is completely sold on the
virtues of the cars.''

An earlier article in the August 3, 1962 Summer Gator was headed

                    ``Prof With Rolls Ain't Royalty''

and read in part:

	``While most `underpaid' UF professors consider themselves lucky to own
a car of any make or vintage, one professor owns four cars.

	And---they're all Rolls Royces, and the result of his hobby,
not his profession.

	Dr. John E. Maxfield, head of the UF mathematics department, owns four
of the Classic cars, two of which are used daily by him and his wife.

	Dr. Maxfield buys Rolls' which are not operating, restores them to
working order, and then sells them.

     	`I never make money; I do it for a hobby,'

he said. 

     	'I guess I make about 10 cents an hour for restoring the cars.'

	Dr. Maxfield would sell his 1927 yellow and black convertible for
about $5,500, but he's not interested in selling any of his cars
until he reconditions a 1930 Roadster which he has in California or
until he has a 1938 Rolls' repainted.

	Dr. Maxfield usually loses interest in one of his cars when it's
restored to running order and then he offers them for sale.  Next he
buys another and enters the `redeem, restore, resell cycle' once again.

	He's been interested in the restoration of Rolls Royces for about 15 years.
He said his hobby always attracts attention and allows him to meet
lots of people.''

A faculty member, Dr. Samuel Gould Sadler, who taught mathematics at the University of Florida from 1954--1972, also spoke with me during the summer of 1995 about Professor Maxfield. Sadler recalled that Maxfield had 6 tons of spare parts for the Rolls Royces and a large garage at his home for the repair work. Sadler recalled that Maxfield's father owned fruit groves in California, which were later sold as California population expansion caused the town first to encroach upon, then later engulf the Maxfield orchards.

Maxfield later told me that his grandfather had been a pioneering Californian, successful in the 1849 Gold Rush. Although this grandfather bought a farm and raised his children elsewhere, he spoke so glowingly of California that all of his children, including Maxfield's father, settled in California. Maxfield's father was indeed involved in farming as Sadler remembered, but as time went on, the increasing smog made farming more difficult, water became more costly as the population of the Los Angeles area expanded, and the taxes increased dramatically.

Gould Sadler was awarded the Doctorate in Education by the University of Florida, defending his thesis in February, 1950. He conducted an investigation ``to establish criteria for awarding grants-in-aid from Federal funds to students on the college or university level''. His Doctoral Committee contained Professors Franklin Kokomoor and C. Basel Smith from the Department of Mathematics. Sadler was still well remembered by some faculty for the creation of a partly humorous scroll, treating events in the history of mathematics. During a visit to the Sadler's home with Theral and Nancy Moore, I had the privilege of viewing this scroll, which Sadler made while taking a graduate course in the History of Mathematics from Dr. Kokomoor. The scroll turned out to be over 20 feet long, rolled up in the oriental fashion, and treated events in both the history of Western and Asian mathematics.

The following biographical sketch is contained in Sadler's thesis:

	``Samuel Gould Sadler was born in Chatham, Massachusetts,
September 30, 1914. He received his public school education in
Mount Dora, Florida where he graduated in June, 1933.  In the fall
of 1934 he entered the University of Florida, attending irregularly
until his graduation with the degree of Bachelor of Science in
Education in August 1940.  He received the Master of Education degree
from the University of Florida in June, 1948.  From June, 1948, to
January, 1950, he continued graduate work at the University of Florida
toward the Doctor of Education degree.

	Mr.  Sadler's professional experience includes five years of public school 
work (two as principal-teacher in an elementary school, the remainder in high 
school as a mathematics teacher) and five semesters as part time instructor in 
elementary mathematics at the University of Florida Mathematics

	From August 1, 1942 to November 11, 1945, Mr. Sadler served in the United 
States Navy as a communications officer.  He served overseas with Headquarters 
Detachment, 8th Fleet for approximately twenty-two months.  He was released to 
inactive duty with the rank of Lieutenant.

	Mr. Sadler is a member of Kappa Delta Pi and Phi Delta Kappa
honorary fraternities and has been active in graduate education

	Mr. Sadler married Doris Isted on August 6, 1938.  They have two
children, [They later had a daughter, Faye.] 
Frank Orin Sadler and Eugene Isted Sadler born December 18, 1939 and
October 9,1942 respectively.''

The Sadler's recalled for me that during Gould's graduate student days, they lived with their sons in Flavet II [ed., Flavet = Florida Veteran] which at the beginning consisted of wooden structures set in an area of unpaved roads. Mrs. Sadler recalled very keenly watching the paving of the roads in that area while they were living in Flavet II.

Sadler recalled a story from his qualifying examination days. In those times, graduate students from different departments all took their written exams at the same time. On the set date, they entered a room and were handled an appropriate envelop. Sadler's exam seemed mysteriously to need various tables. When Sadler telephoned Kokomoor and asked him about this, Kokomoor told him, no he did not need tables, just take his time. Sadler spent 9 hours completing the exam, which turned out to have been for a graduate student in Statistics, rather than himself.

Sadler also showed me his copy of Kokomoor's Mathematics in Human Affairs, which was autographed by Kokomoor himself; this revealed that not only could Kokomoor write on the chalkboard with either hand, as several people have recalled for me, but he also was able to handwrite so that the text would read as if reflected in the mirror. Kokomoor had autographed Sadler's copy of his text in this fashion.

We have mentioned earlier in this chapter the new text for C-42, John Maxfield, Margaret Maxfield, and S. Gould Sadler, Contemporary Mathematics for General Education: Algebra, Allyn and Bacon, Boston, 1963. While the Kokomoor materials used during 1935--1960 had emphasized a historical treatment, the approach here, which would metamorphose into our current course MGF 1202: Fundamental Concepts of Mathematics, was summarized by the authors themselves on [6, pp. i--ii] as follows: (capitalized words were underlined in the original)

     ``                          OBJECTIVES

	When a mathematician helps solve a problem from any applied
field---education, agriculture, engineering, military logistics, chemistry---
or when he develops new mathematical techniques that may some day be used to 
solve problems, how does he go about it? What, in short does a mathematician 
really do?  Most of us are sophisticated enough to realize that mathematicians
are not mere counters or adders, that many mathematicians are even inaccurate 
or slow at arithmetic. However, it is part of one's general education to have 
some idea what mathematicians do, just as one acquires some idea what 
physicists do and what artists do.

	Two main features practically characterize mathematics. They are
ABSTRACTION and structure. 

	To enlarge on what we mean by ABSTRACTION, we look at an example.
It may not matter in a certain study whether we are multiplying the
number-of-rows-of-stars-on-a-flag by number-of-stars-per-row or whether
we are multiplying number-of-passengers-on-airplane by pounds-of-
luggage-allowed-each passenger. The numbers may be different, the ideas
the numbers stand for are certainly very different; yet as multiplication
problems they have an abstract similarity.  It is this very feature that
makes the list of fields using mathematics such a long one, for problems from
missile testing and problems from studies of farm yields may conceal under 
their very different vocabularies a similarity that permits them both to be
attacked by the same mathematical techniques.  Our first job in Chapter 1 
is to abstract the essentials of the arithmetic of whole numbers.

	The study of STRUCTURE in mathematics is an attempt to `see
the forest for the trees'.  With suitable abstractions made, the
mathematician need no longer be confused by information that is to him
extraneous and can study the interrelationships of what facts he has
left.  When he has analyzed their logical pattern he can compare and contrast 
that pattern with others, arising in other problems. In this book we are going
to expose the structure of several different arithmetics, one of them [Chapter
 3] not even requiring numbers, and compare and contrast them with each other.

	Although many of us first meet mathematics as a tool subject, one that
is used to solve problems, it also has standing as a subject of its own.  Just
as the machinists who use machine tools have their own counterparts in those
who apply mathematics to solve problems, so those who invent and construct new
tools for the machinists to use have their counterparts in the mathematicians
who develop new mathematical language and techniques.  Some mathematical
creativity is directly inspired by the needs of the problem-solvers, just as the
work of a tool-maker may be inspired by a direct need of the machinist.  A
mathematician may invent an arithmetic custom-made to solve certain types
of problems. Other advances are made at secondary and tertiary levels, such
as the invention of mathematical techniques that can be used to develop
techniques that can be used to develop techniques.  Some new mathematics
comes into being without even this internal and multi-stage purpose.

	So far as learning mathematics is concerned, a striking feature is the
LANGUAGE of mathematics.  We have to learn many new terms and learn the 
special ways they are used in mathematics.  To see the reason for this we 
need only go back to the keys: abstraction and structure.  To abstract what 
is similar among pines, elms, mimosas, and cedars, we have to have a name for 
the concept `tree'.  Part of our problem in learning mathematics, then, is 
simply learning the generic terms needed for abstraction and then the terms 
needed to describe various structures.

	You may find some of this material so different from any you have read before
that you will question whether it really is mathematics!  If you find yourself
worried by such doubts, check to see whether the material is demonstrating to
you these two features, abstraction and structure, for these represent
the essence of mathematical work.  Also, you may have recourse to the
Introduction at the back of the book during and after your study of
the five chapter for an additional understanding of what mathematics
tries to do. ''

Here is an example of the material covered from Chapter 5; it is shown that the ring of 2 x 2 matrices with rational entries is a ring with unit, but that multiplicative inverses do not always exist. It is remarked that the scalar matrices are isomorphic to the rational numbers, and also ideals are studied. When I asked Gould Sadler about the writing of the book, he told me that he had attended Maxfield's large lectures on the topics, taking notes, then they had all fussed with the exposition.

Another issue which had interested me was teaching loads. On the one hand, Theral Moore recalled teaching 17 hours here during the 1950's, but by the time Kermit Sigmon came here as an Interim Instructor in 1963 and began his graduate studies at Florida, the teaching load was then two courses. Naturally, I was eager to ask Dean Maxfield when he telephoned how this drastic change had been accomplished. He told me that two things had occurred which had so drastically reduced the teaching load for graduate students and faculty. First, Maxfield introduced the lecture-recitation system for the precalculus courses, thus reducing the contact hours of the graduate students. [Recall from the last chapter that Emmet Low had been teaching 4 sections of C-42, then 5 sections of Man in the Physical Sciences.] It was relatively easy to get Federal research grants in the early 1960's Maxfield recalled, so that faculty grants were used to get the faculty teaching load reduced. Finally, when A. D. Wallace was hired in 1963, he brought with him from Tulane a large sum of grant money, which helped in this effort. Any new faculty or existing faculty member wishing to do research could be given a two course teaching load. Toward the end of the Maxfield Chairmanship, the Department won a Center of Excellence award to support graduate students and/or postdoctoral fellows with N.S.F. funding.

By coincidence, an essay by Maxfield's thesis advisor, Ivan Niven, The Threadbare Thirties in [8, p. 209--229] discusses national trends from the thirties through the fifties.

	``Teaching loads were higher in the thirties.  In schools with the Ph.D.
programs, three courses was a common load for younger faculty members,
except at a very few major private institutions with slightly lighter
loads. But four courses was a very common load at institutions with
only a Master's degree program or no graduate work at all.  Emeritus
Professor M. Wiles Keller writes that when he went to Purdue
University in 1936,

`most of the staff taught 18 hours per week.'

	He added that loads of 15 hours were possible, presumably for a few
more scholarly professors. This differential in teaching loads
for scholars was not uncommon: Ralph P. Boas reports that at Duke
University he was given only 3 courses

`as an incentive to research,'

where 4 courses was the nominal teaching load.  Similarly, Abraham
H. Taub writes that he went to Washington University as an instructor
in 1936 with a teaching load of 13 hours a week, where the normal
teaching load was 15 hours a week. He was given a `research'

	According to the AMS Survey ... headed by A. A. Albert,
teaching loads in the midfifties were still around 10 to 11 hours per week
for younger faculty members in the major state schools with Ph.D. programs.

	Department heads in the thirties, secure in positions that they could hold
as long as they wished, rarely consulted more than a small inner circle of
professors, if that, about significant decisions on hiring, tenure, and
promotion. They could control graduate admissions and graduate
assistantships and fellowships, or delegate this control to trusted
colleagues.  Very few departments had a formal committee structure. In
short, department heads could be, and many were, autocrats, benevolent
in varying degrees. This system could be very effective if a strong
department head was brought in to build up a lagging department, to
offset the danger of mediocrity perpetuating itself.  Nevertheless,
there is greater justice in the modern practice of a periodic review
of department heads.''

Niven also writes that the two course teaching load did not arrive at the University of Oregon until the mid-fifties.

The preceding paragraphs leads us naturally to the topic of A. D. Wallace. As a preface, we should also introduce another new senior faculty member, Wayman Strother. The old, faithful 1955 American Men of Science reveals that Strother was born on April 23, 1923 and took the B.S. at Alabama State Teachers College in 1943. He served in the U.S. Navy during 1943--1944, then received the M.S. from the University of Chicago in 1949. After the receipt of this degree, Strother taught at Illinois Institute of Technology as an Instructor during 1949, and had taught at the University of Miami as an Instructor during 1948. He received the Ph.D. in mathematics from Tulane University in 1951 as a student of A. D. Wallace, then after a year at the University of Alabama, went back to Miami as an Assistant Professor in 1952. From 1959--1961, Strother served as the Buckingham Research Professor and also the Chairman of the Department of Mathematics at the Miami University of Oxford, Ohio. During the academic year 1961--1962, Strother came to the University of Florida as a Professor. During 1963, David Foulis, also a Tulane Ph.D., joined the department as an Associate Professor, and offered a seminar on Orthomodular Lattices. By 1964, Strother had left to be the outside chairman at the University of Massachusetts at Amherst, and in 1965 Foulis joined him there.

Alexander Doniphan Wallace was born in Hampton, Virginia on August 21, 1905 and died on October 16, 1985 in New Orleans. Apparently, Wallace worked in the naval shipyards in Hampton, possibly as a draftsman, prior to his entering the University of Virginia in 1931. He took the B.S. degree there in 1935, the M.S. in 1936, and the Ph.D. in 1940. He spent 1940--1941 at Princeton University as an assistant to Professor Solomon Lefschetz, then 1944--1947 as an Instructor at the University of Pennsylvania, before joining the faculty at Tulane University where he was on the faculty from 1947--1963 and chairman from 1958--1963. He came to the University of Florida in 1963, attracted by the opportunity to build up a second department in the South, following his success at Tulane, and served our institution until his retirement in 1973. At that time, according to Professor Al Bednarek, Wallace donated his mathematical books to the department; over twenty years later in 1995, when I idly examined some German volumes in the Walker Hall 201-F lounge and saw ``Don Wallace, 1935'' inscribed on the fly leaf, I found that several of these books still remain with us. As we have seen in Chapter 8, our own Ph.D. graduate Emmet Low attempted to move Wallace to Miami; so Wallace spent 1966--67 in Miami, before returning to Florida to serve as Chairman of our department during 1967--1969, gratefully relinquishing this post in 1969, I suspect, when he received an appointment as the first Graduate Research Professor in the Department of Mathematics, a post he would hold until retirement in 1973. During 1968--69, Wallace also served as President of the University of Florida chapter of Sigma Xi. (The reader may recall that Dean Thomas Simpson had served as President of Sigma Xi during 1941--42, and also our faculty member Professor Herbert Meyer served as President during 1954--55).

Fortunately for our history project, Professor Beverly Brechner organized a Special Session in honor of A. D. Wallace at a 1986 meeting of the Florida Section of the Mathematical Association of American, and a volume containing the invited addresses happened to be located by Kermit Sigmon, a Ph.D. student of Wallace, abandoned in Walker Hall awaiting recycling, whence it came into my possession. Since Beverly was kind enough to organize this session, I will give her the first word, before quoting extensively from the addresses of Professors Robert Koch and Al Bednarek in this volume [9].

In an e-mail message of April 7, 1994, Professor Brechner wrote the following about her recollections of A. D. Wallace:

	``A. D. Wallace hired me when I first came to UF, he was Chair
of the department for one year after I arrived, and remained
in the department for several years after that.  I considered
him a good friend.

	Wallace told me one time (confidentially, but I can't see why it
needed to be confidential) that he was brought to UF to build up the
department. And he certainly made a difference in the attitude of the
department toward quality and research.  He generally went to lunch at
what is now the Holiday Inn on 13th Street, and invited all who would,
to join him.  This had the effect of bringing together members of the
faculty whose paths might not otherwise cross.  Goals of the department
were among the topics of discussion on many occasions.

	ADW was responsible for the Florida Section of the MAA becoming
a section by itself, splitting off from the Southeastern section.
The geographical length of the state made it almost impossible for
the people in South Florida to participate in the more northern
activities of the Southeastern section.  He made sure that top
mathematicians were invited every year, which ultimately contributed
to the success of our section. And our section is considered one of the
most successful of the various sections.

	In addition, he had many Ph.D. students, produced many papers, and
in his time, was considered one of the outstanding mathematicians.  My
mathematical field was not close to his, nor was I interested in what
he was doing. He asked me a topological semigroup question once, and I
answered it after thinking for a few minutes. His reply was: ``You're a
smart cookie. Why are you hiding?''

	Perhaps he meant why wasn't I working in semigroups. For all of the
above reasons, I thought that there should surely be a special session in his
memory, and perhaps it was appropriate for me to do it.''

It was indeed appropriate, and while Professor Brechner has brought up the topic of the formation of the Florida section of the M.A.A., let us quote from Professor Meacham's recollections of this event as he commented on a draft of materials from the early portions of this chapter which I had sent him:

	``Your statement about A. D. Wallace's strong participation in the
1967 meeting of the S.E. Section of the M.A.A. was also very accurate,
but he also gave strong guidance in the rump session of the Florida
mathematicians who wanted to break off from the Southeastern Section.
We felt that the geography of Florida needed to be acknowledged by
setting up a smaller region.  One of our aims was to induce secondary
school teachers to join with us in making an effective Florida Section.

	There were five or six or so from Florida State University, about
the same number from the University of Florida and a bunch more from
the other colleges and  universities in Florida.  I did not list more
than the first set of officers because I did not want to offend by omission
many others who participated in the meeting and signed the original
petition to the parent organization (Mathematical Association of

Professor Robert Koch of Louisiana State University provided the following comments on A. D. Wallace's influence on Tulane University during the time period prior to his departure in 1963 for the University of Florida, [10].

	``Professor Wallace was known to his friends and colleagues as
Don. But it was many years after finishing up a Ph.D. with him before
I was able to call him by his first name.  This was due to the nature
of our relationship, and not to his formality.  He was, in fact, very
relaxed, open and friendly.  But this was combined with a great
personal dignity.  He was a very respectable person, a gentleman of
the old South, a devoted family man, a man of high personal and
professional standards, a stable and strong personality.  He did not
tolerate abuse. I recall once when as a student I greeted him one
morning with `Good morning, Prof.'. His immediate reply was `Good
morning, Stude'.

	He was what I would call a very mature person, in the sense that he
had learned to control his emotions, and did not seem to indulge
himself in excessive worry. He told me once that his major Professor,
G. T. Whyburn, used to say  `do not fret about those things you are unable
to influence.' or something close to that.

	In mathematical things he was always encouraging.  I don't recall his
criticizing any of his students work, except in the way of making helpful
suggestions. I do recall his referring to a paper once as `stillborn' but
this kind of remark was his way of expressing a professional opinion, and
not an offhand condemnation. He was very stimulating to be around and very
constructive.  He always had unsolved problems to suggest.

	I don't know very much about Wallace's early life.  He was born in
Hampton, Va. in 1906 and went to the University of Virginia, where he
received the Ph.D. degree in 1939. He worked under the direction of
G. T. Whyburn, one of R. L. Moore's many distinguished students.  He spent
a few years as an Instructor at Virginia; some of his colleagues were
D. W. Hall, J. L. Kelley, and G. E. Schweigert, all Ph.D. students of Whyburn.

 	During this time period he wrote about a half dozen papers,
dealing with monotone transformations, boundaries, fixed points, cyclic element
theory.  In short, the kind of mathematics dealing with mappings and
structure of continua which Whyburn students probably all inherited a
taste for.  But Whyburn's interests also encompasses Algebraic
Topology, as one sees in reading his Colloquim book.

	And so it was that Wallace went to Princeton, and served a year as
Lefschetz' assistant.  It was during this period that Wallace developed an
expertise in Algebraic Topology.  He took an Assistant Professorship
at U. Pa. in 1941. In 1946 he gave an invited address to the AMS in
New York City in which he outlined a modified approach to the
Alexander cochain complex.  This suggestion was brought to fruition by
E. H. Spanier in his dissertation (U. Mich. 1947) `Cohomology 
theory for General Spaces', Ann.  Math. 1948, 407--427.  This
theory, which agrees with Cech cohomology theory (see Spanier's book
Algebraic Topology), has become known as AWS (Alexander-Wallace-Spanier)

	In 1947, W. L. Duren succeeded H. E. Buchanan in the chairmanship
at Tulane, and revitalized the long-dormant graduate mathematics program.
Duren had the vision of building up graduate mathematics, with the help
of newly emerging Federal grant support of basic research. Tbe National
Science Foundation had just been formed by Truman, and other
research-supporting agencies were beginning to form. Duren recruited
A. D. Wallace from U. Pa. and B. J. Pettis, who had been a Ph.D. student of 
E. J. McShane at Virginia, as the nucleus of the program. Indeed, the
University of Virginia had revitalized their graduate mathematics
program in a similar way 12 years earlier.  Wallace at the time was an
Assistant Professor, and the offer was an Associate Professorship.
Wallace took the offer to his Dean, who promoted him on the spot.
Duren offered him a full Professorship, which he accepted. This move
away from the Mathematical centers of the North-East must have required
great vision and courage.  But it is in keeping with Wallace's often
stated goal of building up Mathematics in the South, a goal to which he
remained devoted throughout his entire career.

	The Mathematics Department was housed in Gibson Hall, one of the
oldest buildings on campus, on the second floor. This building also
housed the Philosophy department and on the 3rd floor was a museum
(stuffed birds, I think.)  The entrance to the 3rd floor was gated
off, so we could only wonder what was up there.  About 1960 the
Mathematics Dept. moved to the 3rd floor, displacing the birds who
knows where. I recall Egydio de Castro e Silva, who was on the music 
faculty of Newcomb College, close to where Wallace lived, and who was
expert in the music of Villa-Lobos.  Wallace loved classical music,
and listened a lot to the phonograph.  He had a grand piano in his
home, but I don't know who played it other than his daughter, who was
taking piano lessons. He was also an avid reader, and a long-time
subscriber to the New York Times Book Review.

	His teaching style was what one might call modified Moore.  That is, a
do-it-yourself approach, in which chunks are handed out for the student
to prove (with no outside help).  Most of Wallace's family tree have
followed this technique, with, I think, very good results.  It seems to
me there is something very basic about the method.  Not only does it get
students in a research spirit, but the student presentations constitute an
effective teacher-training experience. 

	At an AMS meeting about 15 years ago, there was an invited hour speaker
who spent the hour telling the audience that his newly written book was
too technical to talk about.  Wallace chaired a later session, and
announced to all his `principle of the bite-sized chunk', according to
which one breaks the subject down into small, expoundable pieces.  Well,
this is how he taught Algebraic Topology to generations of graduate
students at Tulane. His notes, which had been carefully prepared over
several years laid it out in small, do-it-yourself pieces.  Imagine
teaching Algebraic Topology to someone who does not know what a group is.

	This reminds me of my first exposure to Wallace.  I was an incoming
graduate student, walking into the office for the first time.  Here was
this older man with a mustache and crew cut, and a pipe held together by
wires, sitting with his feet propped up on the desk, two or three
people standing around. He was saying 

	`Consider the set of all functions from the unit interval to itself.'

	My jaw dropped, and I thought to myself, Good heavens,  what is that?
The recollection reminds me of a Gary Larson cartoon. It seems to me
that it is quite common to return to first mathematical influences,
and if so, I guess I'm lucky that Wallace's first words were not even
more abstract.

	Wallace was an Episcopalian.  I do not know how much of an influence religion 
was in his life; the subject never came up between us.  He was a man
apparently free of any noticeable prejudices.  He once told me of his
plans to hire a mathematician I know.  I responded, 

	`Dr. Wallace, you'll never get along with this man.'

His response was:

	`I can get along with anybody.'

	And I believe he was right. He was understanding enough to accept
shortcomings, and was forceful enough and convincing enough to lead
things in his direction.  This was the role he played at
Tulane---to a large extent he influenced the direction of the
department.  This might have been very difficult to do except for the
guiding wisdom and understanding of Bill Duren.

	He championed seminars, not only his own, but general
department-wide seminars in which everyone, including students,
presented papers.  Of course, this was in the earlier days at
Tulane, when there were a half dozen active faculty and about
20 graduate students.  It was a close-knit group.  Departments
nowadays (e.g. LSU, UCLA) have gotten to be more like 4 or 5
subdepartments, and its a lot harder to have the family spirit
that prevailed at Tulane.  Each morning he made the rounds 
of the graduate students, saying

	`What have you proved for today? Remember, A theorem a day brings
promotion and pay!'

	For the more advanced students there was always the threat to change one's
grade. Wallace had two Ph.D. students at U. Pa., who worked in topology,
[ed., both prior to 1946] C. Saalfrank and G. Butcher.
His first students at Tulane all worked in set theoretic or Algebraic topology.
The later ones were mostly in Topological Algebra and Partially ordered 
(1950) W. Conner Separation axioms
J. W. Keesee Algebraic topology (exact sequences for triples)
(1951) W. L. Strother Multi-valued functions (continuity, coefficient group)
(1952) Haskell Cohen Algebraic Topology (cohomological dimension)
W. Gordon Algebraic Topology (dependence on coefficient group)
C. T. Yang Algebraic Topology (relations with Cech theory)
(1953) C. E. Capel Topology (inverse limit spaces)
R. J. Koch Topological Semigroups
L. E. Ward, Jr.Partially Ordered Topological Spaces
(1954) W. M. Faucett
I. S. Krule Quasi-ordered Topological Spaces
(1956) L. W. Anderson Topological Lattices
     It was Wallace's custom to assign as a dissertation project an
area, rather than a specific problem. It was easier to get started,
and opened the door for further work after the dissertation.  He
frequently served as an intermediary for his students, trying to get
them offers if they seemed disgruntled, encouraging them to apply for
contract support, corresponding with them, and in general being fatherly
about their careers.  Of course, this was in the days when the market was
open.  He had numerous connections around the world.  Indeed it was
through those connections that he was able to attract A. H. Clifford,
Karl Hofmann and Laszlo Fuchs to Tulane in later years. 

	... In 1955 he gave an invited address to AMS in Baltimore,
entitled `The Structure of Topological Semigroups.' It was on this
occasion that a local newspaper article carried the lead:
`Mathematician says 'Mob is Map.'. (Mob was Wallace's nickname for
topological semigroup; he was fond of short names, e.g. `act', `bing,'
` clan.')

	We made several trips to meetings during the period
1949--53 and 1955--56 (when I visited for a year on
the occasion of A. H. Clifford's arrival, and Wallace's first year's
course on Topological Semigroups).  Wallace did not drive a car at
that time; he learned that skill after retirement from Florida in
1973. So Strother, Wallace, myself and one or two others made several
trips to MAA and AMS meetings within driving range.  He wanted to stay
in touch with his neighbors. Wallace was always entertaining at
meetings.  His style was outgoing, and he did not allow things to drag
very much---he would interrupt with questions or suggestions
and bring the meeting to life.  He was especially lively when chairing
a session.  One was not safe sitting idly in the audience---he was liable
to direct a question to you after the talk.  One had to stay alert.

	In addition to his published work are several sets of lecture notes,
some of which have had wide distribution and considerable influence on
generations of mathematicians.  Some of these are: Notes on Algebraic
Topology; Notes on Topological Semigroups; Relation Theory.  In 1969
and 1971 Wallace organized conferences on semigroups and automata at
U. Fla., from which there were 2 volumes of Proceedings.  He served as
a member of CUPM and SMSG.  He was elected Governor of the MAA, and served
on the Council of the AMS.  He served on the Editorial Boards of Summa
Brasiliensis Mathematicae, American Journal of Mathematics, and
Semigroup Forum.

	For those of us who were touched by his personality he was our hero,
our leader, our friend.  The bite-sized chunks he dispensed were
little gems, pointing in the direction of larger, nobler goals.  His
trust and encouragement were a source of great strength.  The Greeks
said it:

`without trust there can be no love.'

	We all loved him, and still hold him in mind as a continuing
inspiration in our studies. The fundamental structures whose beauties
he revealed to us are now our treasures and our responsibilities to develop.'' 

I queried Professor Kermit Sigmon about this terminology above, and he replied in an e-mail message on November 1, 1995:

``... `mob' was just his shorthand for a general `topological
semigroup.' And `clan' was his shorthand for a compact, connected
topological semigroup with identity ... `a mob with a leader', as best
I recall.''                    

Professor Alexander R. Bednarek was born on July 15, 1933 in Buffalo, New York. He did his undergraduate work at the State University of New York at Albany, graduating Magna Cum Laude in 1957, then taking his graduate work at the State University of New York at Buffalo, where he received the Ph.D. in 1961. He spent 1961--1962 as a Senior Mathematician at the Goodyear Aerospace Corporation in Akron, Ohio, before returning to academia the next year, as an Assistant Professor at the University of Akron. He joined our department in 1963, the same year A. D. Wallace came to the department. He has worked both with A. D. Wallace and his successor as Graduate Research Professor in the Department, Stanislaw Ulam. This later association led to Bednarek's serving as a visiting staff member in the theoretical group at Los Alamos National Laboratory, T-Division, as it is called, during 1976--1984. Professor Bednarek would serve as the first Associate Chairman of the Department during 1967--1969, then serve over 15 years as Chairman, from 1969, when he was in his mid-thirties, until 1986, and then again during the spring term of 1988. During his years as chairman, Bednarek was one of the organizers of two symposia held at Florida on Automata and Semigroups in 1969 and 1971, a conference on Finite Groups held in 1972, and two International Symposia on Dynamical Systems, held in 1976 and 1981. His association with Ulam has led to his serving on the editorial board of the Ulam Quarterly since 1989 and also to co-editorship with Mrs. Francis Ulam of an anthology, Analogies between Analogies, concerning the life and times of Stanislaw Ulam, published by the University of California Press in 1990.

Here is how Bednarek described in his own words A. D. Wallace at Florida as well as Bednarek's coming to Florida, cf. [11]

	``My tribute to Professor Alexander Doniphan Wallace will be sprinkled with
anecdotes from his years in Florida.  It is my hope that these will form a
montage that conveys his humor, his spirit, his generosity and his contributions
to the mathematical life of the University of Florida and to that of
the mathematical community in the State of Florida.

    Those of you who had met him undoubtedly remember him as a rather
formal individual---the women who met him will remember having
their hands kissed. Some considered this demeanor a pleasant
affectation.  For example, I believe that he enjoyed being called
`Don'---even by those his junior.  It is by this sobriquet
that I will refer to him in what follows.

	How did Don come to Florida?

	In the early 1960's the University of Florida made a significant
effort to build up the physical sciences, engineering and mathematics.
Dr. L. E. Grinter, then graduate dean, had initiated his ``graduate
research professorship' ---a faculty rank with perquisites
designed to attract renowned scholars to our faculty.

	A Tulane student of Don's, Wayman Strother, was a member of the
department of mathematics at the University of Florida.  He learned
that Don might consider leaving Tulane if the terms were attractive.
Wayman and John E. Maxfield, the chairman of mathematics at UF, made
a trip to New Orleans to discuss the matter with Don. (Incidentally,
Don always claimed that the middle initial `E' in Maxfield's name stood
for `elongated'---John is at least six feet four inches tall.) As it
turned out, the terms were rather severe, and when our president
transmitted them to the Board of Regents and they, in turn, transmitted
them to the Cabinet acting as the Board of Education, they were rejected.

	Fortunately the University of Florida had a friend on the Board who
was interested in seeing this project materialize.  He arranged for
Maxfield to come to Tallahassee and to present his case to Governor Farris
Bryant and to his Cabinet. The obstacle was Don's salary.  Maxfield had
proposed a salary exceeding that of the Governor.  While Governor Bryant
had no objection, there was one member of the Cabinet who thought it
`unseemly' that any state employee receive a salary majorizing the
Governor's.  A compromise, satisfying the Cabinet member in question and
supported by the Governor, was reached.  The National Science Foundation was
to be approached to provide one-half of Don's academic year
salary. This was done, and for at least the first year, the Foundation

	Since Florida is a `sunshine law' state, no confidence will be breached if I
tell you that Don came to the University of Florida in the fall of 1963 for an
academic year salary of $25,000.  Moreover, this was a 10 month salary since
we were then on the trimester system and the academic year was also `elongated.'
Shortly after moving to the University of Florida, Don attended a meeting of
the American Mathematical Society in Miami. He was approached at a
social gathering by a well-known and, on this occasion, `well-oiled'
mathematician who asked  him whether it was true that his salary
exceeded the governor's.  Don responded,

	`Yes, however, there are fifty governors but only one A. D. Wallace.'

	When Don came to Florida, his mathematical interests were focused on
topological relation theory.  He had directed several dissertations in this
area at Tulane. Wayman Strother's was one. Strother examined various
extensions of the concept of continuity to topological relations.  It was
Don's intention to gather a group to explore, under his scientific
leadership, these extensions of function theory and relational

   Don persuaded David Foulis, now at the University of
Massachusetts---then at Wayne State University, to join in this
enterprise.  At that time, David was working in lattice theory.  He
came to Florida in the fall of 1963 bringing with him a number of
graduate students---some quite talented and all uniformly

   I never did determine how Don learned of my interest in this subject
since I was not then personally acquainted with him.  I suspect that he
refereed a paper of mine that was to appear in Fundamenta
Mathematica.  Risking the appearance of a personal indulgence, I would
like to relate how I met Don and how I came to be invited by him to join
the mathematics department at the University of Florida. I do so in hope
of elucidating his modus operandi.

	Following graduate school, I accepted a position with a midwest
aerospace corporation [ed., Goodyear Aerospace] where I spent
a little over one year practicing, what I like to refer as,
`preventive mathematics.' Frustrated by the disconnected character of
my assignments, missing teaching, and not wanting to undertake a major
relocation, I joined the faculty of a small local university.
 [ed., Akron State] I bought, and moved into, a new `old'
house in December 1962.   In January 1963 I presented a paper at the
annual meeting of the AMS held at Berkeley.  Someone told me that Don
wished to speak with me.  Since I did not know him, nor what he looked
like, we were introduced by a mutual acquaintance. Don and I discussed
mathematics and he told me that he was moving to Florida in
the fall.  At no point in the conversation did he suggest that there
might be an opportunity for me to do so.  One month later, I received
a formal offer to come to UF.  The offer included a teaching load
one-half my load at the time and a modest salary increase---even more
modest than I realized when I later discovered the `elongated' academic
year.  I accepted without visiting UF---for that matter, without having
been in Florida.  The promise of greater professional opportunity and
excitement was sufficient.  This promise materialized.

	When Don arrived at UF in the fall of 1963, he initiated a lively seminar in
Relation Theory.  As was his habit, he had the notes of this seminar
transcribed. Mrs. Lin---now Professor Lin at the University
of South Florida---was the official `scribe.'  In perusing her
notes, the works cited included those of: M. Stone, E. Zermelo,
M. Zorn, G. Birkhoff, H. Vaughn, T. Szele, E. Witt, G. Schweigert,
C. Berge, O. Frink, M. M. Day, R. Koch, E. S. Wolk, and, of course,
A. D. Wallace. These citations may give you a feeling of the thrust of
this activity.  It represented a fusion of the algebraic, set
theoretic, topological and function theoretic perspectives.

	What was Don trying to accomplish?

	My response to this question is based in part on fact and is in part
speculation. Don was G. T. Whyburn's student.  There was, as a
consequence, a natural connection with the Polish school of topology.
Aside from this natural scientific connection, I believe that Don was
intrigued by the `sociology' that resulted in the emergence, and the
continuation, of the Polish mathematical tradition.  A reading of the
autobiographical works of M. Kac, K. Kuratowski,
and S. Ulam supports the contention that a conscious decision was made
to concentrate the talents and energies of Polish mathematicians in the
areas of general topology and functional analysis. That the Polish
mathematical tradition survived the devastations of World War II is
attributed by many to that decision.

	It is fair to say that the successful development of the department of
mathematics at Tulane University, in which Don played such a dominant
role, mirrored---though on a smaller scale---the
Polish model.

	It was this success that Don hoped to replicate at UF. He had chosen an area
that allowed for a reasonable entry level to mathematical research and
that could benefit from his algebraic and topological expertise.

	The experiment failed!

	There is no clear single reason for this failure.  There are, however, a few
identifiable contributing factors.

  1. Don's `partners' were very much junior to him. While he enjoyed the role of mentor, their inexperience didn't help.
  2. The direction of effort was too diffuse. It is difficult to imagine parts of mathematics that could not be subsumed under the label of `relation theory.'
  3. The early and mid-sixties were periods of considerable mobility in the mathematical community. This, coupled with a certain amount of administrative instability, led some, who could have contributed to this program, to come and stay but a short time.
Nevertheless, it was an exciting period in our department's history. As mentioned earlier, Don initiated a very active seminar. A stream of visitors, especially from the Eastern Bloc countries, provided a powerful and exotic stimulus. The list of those from Poland, for example, reads like a veritable `Kto jest kto' (Who's Who in Polish) of Polish mathematicians. Don and his wife, Willie-Catherine, were gracious and generous hosts. Their parties, occasioned by these visits, were open to all---graduate students as well as faculty. Just as `a theorem a day brings promotion and pay' served a Tulane as a gentle prod toward activity, its Florida analogue was, `Professor X, what have you done for our beloved discipline today?' I frequently responded, `A great service---I stayed away from it.' As the appended list of Don's Florida doctoral students reflects, in the mid-sixties his mathematical activity was once again focused on binary topological algebras. In addition, he brought his formidable topological expertise to bear on the area of functional equations---simplifying and extending many results that up until that point had been of an algebraic character and whose proofs had depended on algebraic techniques. In the fall of 1966 Don moved to the University of Miami. I do not know the particulars of his activities there. If I recall correctly, it was during that period that he helped engineer the appointment of Laslo Fuchs to that faculty. The year 1967 proved to be a benchmark in the saga of the UF department. John Maxfield, who had been toying with the idea of leaving Florida for some time, accepted the chairmanship of the mathematics department at Kansas State University. Don was persuaded to return to UF as chairman. Since he was obligated to Miami for the academic year, he appointed a recruitment committee at UF to handle appointments for the 1967--68 academic year. I served as secretary. As mind boggling as it may seem, that spring we hired 17 faculty members and 5 postdoctoral fellows---all sight unseen. Four members of that charter group remain and are presently active full professors. [ed., James Brooks, David Drake, Jed Keesling, and Arun Varma (ed., deceased in 1995)] Although Don exercised considerable influence in the department during the 1963--66 period, he had no formal administrative responsibilities. It was intriguing to watch him discharge the duties of the new office. It should be noted that, essentially, there was no cadre of active senior faculty to assist him. Don was fond of `labeling' the committees that he formed; for example, GradCom (graduate committee), ExCom (executive committee), etc. Once some of us distributed a huge memorandum constituting the ultimate committee---KingCom. It was around this time that Don, along with several others, initiated the move to form the Florida Section of the Mathematical Association of America. The first meeting of this section was held in 1968. Don's mathematical activity at this point centered on what he called `acts' or `topological automata.' By this he meant a topological semigroup T, a topological space X and a continuous `transition' T times X rightarrow X satisfying t_{1} (t_{2} x) = (t_{1} t_{2} )x for all t_{1},t_{2} in T and x in X. Given the dominance of digital computers some objected to this generalization of `automata.' In view of the current interest in computation in homogeneous media, e.g., optical or acoustical computation, Don may very well have been prescient. In 1969 we held the `First Florida Symposium on Automata and Semigroups.' A second symposium on the same subject, dedicated to Don, was held in the spring of 1971. Professor R. J. Koch prepared a tribute to him on that occasion. Don relinquished the chairmanship of our department in 1969. [ed., to become the first Graduate Research Professor in the Department of Mathematics] I succeeded him in this post. [ed., and Zoran Pop-Stojanovic later in 1972 succeeded Bednarek as Associate Chairman and Kermit Sigmon became the first Director of Graduate Studies] It had become clear at that time that the disciplinary emphasis in our department had to change. Given the size and complexity of the University of Florida, demands for mathematical support from various corners of the campus were increasing. Don was not completely sympathetic toward these shifts. He used to annoy some of our engineering faculty by pointing out that he was an `applied mathematician' since he `applied algebra to topology.' Don continued his researches in topological algebra and directed three additional doctoral dissertations in this field prior to his retirement in 1973. Upon the occasion of his retirement, a tribute was prepared. I'd like to close my remarks by quoting a part of it. `Ever-mindful of the tradition of academe, his spirited perorations in their defense will be missed by the many groups whose gatherings were enlivened by the same. Don and his wife Willie-Catherine will be moving to New Orleans where we hope that they will spend many happy years indulging their particular tastes for: (1) overseeing the proper `rearing' of their only daughter's (Alexandra's) children, (2) fine food, (3) southern architecture, (4) `lettering the editor' and (5) science fiction.' I sincerely hope this was so!''

Professor Beverly Brechner has recalled for me that in addition to the well known

	``A theorem a day merits promotion and pay'', that A. D. Wallace
was also fond of the saying ``A lemma a week is all I seek.''

Professor Bednarek has also commented to me that Wallace was well known in the Gainesville community for his letters-to-the-editor in the Gainesville Sun.

Here is the listing of A. D. Wallace's Florida doctoral students:

1964 Lin, You-feng
Theorems on Topological Semigroups
1965 Lin, Shwu-Yeng Tzeng
Relations on Spaces
1966 Borrego, Joseph Thomas Jr.
On Borsuk's Paste Job and Related Topics
1966 Choe, Tae Ho
Compact Topological Lattices
1966 Kermit, Sigmon
Topological Means
1967 Shershin, Anthony
Results Concerning the Schutzenberger - Wallace Theorem
1969 Khuri, Andrawas
Applications of Papkovitch Functions to Three-Dimensional Thermo Elastic Problems (this dissertation was originally directed by C. B. Smith, but Wallace saw it to its formal completion following Professor Smith's departure from the University of Florida).
1970 Chae, Younki
Topological Multigroups
1970 Robbie, Desmond
Some Theorems on Binary Topological Algebras
1972 McGrannery, Clark
Boundary Points in Real Topological Semigroup Acts

The first student on this list, You-Feng Lin, had begun his studies at Tulane, and offered the following recollections of A.D. Wallace in [12]:
	``On the 26th of September, 1959, after the school had started for
one week, I nervously walked into Professor Wallace's office in the
third floor of Gibson Hall in Tulane University.  Before I finished
apologizing for my late arrival due to reasons beyond my control, he
signed my registration card and quickly handed me a stack of notes known
as AT-1 (Algebraic Topology 1).  AT-1 was a core course for the Tulane
math graduate students, taught using the so-called Texas system 
(or R. L. Moore's System) by Professor Wallace.  The notes contained only
Definitions, Propositions, and Theorems without proofs. We the 
students were expected to present, to the class, our proofs of the
Propositions and Theorems without outside help. Professor Wallace,
overlooking every face from a seat against a side wall, would call
students one by one to the board to present their work.  During the
student's presentation, he would encourage questions and participation
from the audience, and often made encouraging comments or critical remarks.
Omissions of statements as being trivial or obvious were never allowed.
He said:

		`If an assertion is obvious, it may be proved easily and quickly.'

	The AT-1 class was always lively and everyone participated fully with
proofs, counter-examples, questions and answers.  There was no
`handwaving' that ever got Professor Wallace's approval.  He never
gave any help or hint even when no one in class could give a correct
proof. Needless to say, AT-1 was the toughest and most challenging
class for me (and probably for everyone else).  As it turned out, it
was also a rewarding experience for me.

	I had heard senior grad students' fear of facing Professor Wallace's

		`Ah, Mr.___________ , tell me what you have done lately?'

	To avoid embarrassment, we usually shied away from him whenever
possible.  It was the afternoon of Thanksgiving Day in 1959, the third
floor of Gibson Hall was very quiet, but not empty; as I was strolling
down the hallway trying to find a student to chat with, Professor
Wallace suddenly stepped out of his office and greeted me:

		`Ah, Mr. Lin, tell me what have you learned from AT-1?'

	I hesitantly stammered:

	`I like the Wallace Theorem and believe it to be true even for an
infinite product of compact sets in the infinite product space.'

	 At first, Professor Wallace thought it wouldn't be true in the general
form, but after listening to my shaky hand-waving attempt to prove it, he
told me that he would like to see a written proof.  The next day I handed
him my proof.  He read it quickly, then gave me a big hand shake 
and an approving smile. My fear of Professor Wallace disappeared.''

This proof by Lin appeared as ``A note on the Wallace Theorem'', Portugaliae Mathematica, 19 (1960), pp. 199--201.

Dean John Maxfield offered me his own version of these events in our telephone conversation of March 16, 1994 which I recorded shortly thereafter as follows:

	``An important person in helping build up the department was Wayman
Strother. Strother, who came as a Professor in 1961, knew A. D. Wallace
at Tulane. Strother also brought in David Foulis.  Strother knew Marshall
Stone and Deane Montgomery at the Institute for Advanced Study, so they
tried to help in the building efforts.  Strother also got A. D. Wallace
interested in coming. But obtaining the offer for A. D. Wallace at $25,000
was a non-trivial political task, since such high level appointments were
passed on not only by the Board of Regents and the Governor, but also
the Cabinet.''

Fortunately, one of the Regents was very supportive of the effort, but still Maxfield had to appear before the Governor and Cabinet. The Attorney General was most opposed, but Maxfield doctored things up so that with grant money, during the first year, the portion of the salary supplied by the state was less than that which the Governor earned. Also Wallace would bring a great big grant with him and would not need to be paid summer salary. Thus the appointment was able to be pushed through.

``With Wallace here, we had a bridge to improve the research climate.
Wallace had a large chunk of grant money and connections to Europe
and Eastern Europe.''

Both current faculty members Kermit Sigmon and David Drake, who were at Florida during these years, benefited from these visitors by developing connections with European mathematicians. I asked Kermit if he could recall some visitors names for me, and he responded with the following list off the top of his head, which had been here one academic year during the 1960's:

Horst Herrlich topology    Bremen
Dieter Biallas geometry    Hamburg
Guenter Graumann geometry    Hamburg, later Bielefeld
Kay Soerensen geometry    Hamburg
Hans Seybold geometry    Munchen
Karlhorst Meyer geometry    Munchen
K.-J. Weinert algebra    Clausthal.

Maxfield had his own little Wallace story for me from the Wallace chairmanship years that is somewhat reminiscent of the ``applying algebra to topology'' quotation Wallace liked to use with the Engineers. We had developed through Kenneth Kidd, a nice connection to the Mathematics Education Ph.D. program in which we had courses in Modern Geometry and in Number Theory which these graduate students would take. Wallace assigned these courses to a visiting Swiss and a visiting Austrian professor respectively, but did not bother to give them any guidance on the level of the courses. When Kidd came to complain about this disastrous teaching, Wallace told Kidd that he would not reappoint these two men to these classes. But then Wallace simply switched the courses each taught, again with disastrous results, and basically killed this connection with the Ed School.

In a letter of May 1, 1996, Professor Wayman Strother offered his own perspective on A. D. Wallace appointment.

	``A number of people have given me credit for contributing to the
hiring of Professor A. D. Wallace.  Both Maxfield and Day mention that
I was involved with Dr. Wallace and Professor Maxfield was involved with
the University and State.  That's worthy of underscoring.  Each of us
contributed an essential link in the chain.  Professor Maxfield's
administrative style made for perfect meshing of these two links.  The one
link to which I contributed was most visible but the many University links
he forged in the background far outweigh. Even department heads experienced
in facilitating the movement of appointments through the machinery of the
University may not find it easy to appreciate what he did.  Appointments
near the stature of people previously appointed in the department or
University don't happen automatically but require the department
head's effort to make the machinery work.  I submit that the universities by
and large have faculty of the highest quality their machinery is designed for.
I say that because I believe it is safe to assume that dedicated members of
every department will have sought the upper limit and made
appointments there.

	An appointment at a quantum leap higher level than the University's machinery
was designed for, required the support of people I had never heard of in the
context of University administration.  That his appointment had to be taken to
the Secretary of Agriculture and his approval sought, for example, was
a surprise to me! Unlike the President of the United States who
appoints his Cabinet and can take action opposite from their
recommendations if he wishes, certain elected officials in Florida are by statute
members of the Governor's Cabinet and there
are things the Governor cannot do without their approval.  I believe they first
turned this appointment down and Professor Maxfield went to the next
meeting with the Governor and persuaded them!  Though Professor
Maxfield administered in an open style and I paid attention, I did not
fully appreciate the complexity of his task until I tried doing it

	There has been some speculation about how Professor Wallace was persuaded to
come from Tulane to Florida.  The speculation is fairly well on target with the
exception of the fact, indicated above, that things have been credited
to me which should have been credited to Maxfield and me.  But in
retirement, I will, for the first time, attempt to verbalize some
items on which I had maintained my own counsel.  

	My contribution to the hiring of gifted mathematicians was based on a simple
truth.  They give much weight to the question 

		`Where will I be a better mathematician?

		Where will I contribute most to mathematics?'

	For some of the best, that question is all important.  Accordingly my
recruiting efforts at Gainesville and elsewhere were not stimulated by
rumors of availability.  When I saw that the department I was in could
provide real opportunity for someone to be a more productive
mathematician, I just assumed it would be worthwhile to approach him
with the idea of moving.

	I had not heard from Professor Wallace or from anyone else that he might 
consider leaving Tulane.  I only reasoned that he might.  Some years earlier 
Tulane had undertaken to make a large scale improvement in the quality of
their mathematics department and their efforts were fruitful.  He was a major 
contributor to that successful endeavor.  I thought his largest contribution 
to mathematics was his own research and his second largest was his influence 
on a department which produced Ph.D.'s who produced mathematics. [I later read 
that for some time a larger percent of Ph.D.'s from that department published 
mathematics than from any other mathematics department in America.]  I thought 
his own research had become largely independent of location, and that
his secondary interests could flourish at the University of Florida
now as it had a Tulane earlier.

	The University of Florida was undertaking an ambitious expansion and
upgrading of its doctoral program in mathematics at the same time that many
other universities were trying to do the same.  There was nowhere enough
qualified faculty to carry out the planned expansion of all of those
programs at once.  For a program to succeed it was necessary for it to
distinguish itself from the others, including others with as much

	I do not disagree with Professor Bednarek's statement about the salary
`as it turns out the terms were severe---$25,000,' 

but would like to say that if he were to replace the word severe by the
word optimal, he would get a another true and pertinent statement.
Negotiations about a $25,000 salary in 1963 showed the department that the
University was serious about building the department.  Negotiations about
his salary showed the University that the State officials were serious about
their interest in the University. The salary exceeding the Governor's got media
coverage which informed the mathematicians of America that our State
was serious about a doctoral program, as a salary one dollar below the
Governor's would not have.  Had the offer been trimmed below the
Governor's salary we would have been without all the above assurances
concerning support for mathematics and I would have exerted every
possible effort to persuade Professor Wallace to reject the offer and
stay at Tulane.

	Having said the offer was optimal, I am obliged to say why it was neither 
too high nor too low.  That it was accepted is another indication that it was
high enough.  Had we asked the University to exercise itself that strenuously
without success, that would have been damaging to our department, and
to others, in the future.  Similary, having a mathematician exercise
himself over an anticipated offer and then fail to make that offer is
damaging to future hiring efforts.  John Maxfield must have studied a
man and studied the University well enough to know whether there was enough
negotiating room for an agreement to be possible, before over-exercising
either party.  He didn't often set in motion a
special appointment which aborted.  We both knew this would not be an easy
decision for the University and would not be an easy decision for Professor
Wallace, but we thought it could be a good decision for both.''

During my conversation of January, 1966 with Dean Maxfield, I had the opportunity to ask him about his relocation to Kansas State. He told me that the main straw that broke the camel's back in terms of his leaving Florida was an administrator's strong opposition to his traveling to Moscow for a month to attend the International Congress of Mathematicians when this was being held in Moscow in the summer of 1966. At Kansas State, they had had a doctoral program in chemistry and physics, but no doctoral program in mathematics. In order to retain a certain type of outside grant in these two fields, Kansas State was required to offer a Ph.D. program in mathematics as well. Maxfield was hired to establish the doctoral program in mathematics, and as some current Florida faculty recalled, Maxfield took some of the Florida professors with him to Kansas State over a period of several years. Maxfield also recalled a little problem with the pre-renovated Walker Hall which was not mentioned in the {\it Alligator\/} articles quoted earlier in this chapter; when it rained, the coeds tended to slip and fall on the worn Walker Hall stairwell discussed earlier. Mautz came over to investigate this problem one day, and slipped and fell on the stairs himself.

Many people have commented to me on Wallace's fine command of the English language and have recalled how receiving a memorandum from Chairman Wallace could send one scurrying to a dictionary. Mrs. Pirenian recalls Zareh laughingly showing her a memo Wallace issued during the throes of the Vietnam War Protest on campus, at which time, some of the English faculty apparently were dressing rather sloppily, possibly in solidarity with the anti-war movement. In this memo, Wallace ordered all faculty and graduate students to dress with all due sartorial splendor for their classroom appearances. In spite of my inquiries, however, no one had saved any of these wonderful memos. Fortunately, for our keener appreciation of what they were all talking about, I located in the University Archives in Smathers Library, the text of an address which A. D. Wallace delivered at the fall initiation banquet of the Phi Beta Kappa on December 2, 1971. This address has been reproduced in full in Appendix A to this chapter, and it gives a sample of Professor Wallace's powers with the English language.

We are now fortunate to have recollections of two mathematicians, Jane Maxwell Day and Kermit Sigmon, both of whom did their graduate work at the University of Florida during the Maxfield Chairmanship. Professor Sigmon told me

	``Professor Wallace sparked more of a research climate in the department.
He made sure that the department had a full program of seminars and colloquia.
He instituted a Journals Seminar for the graduate students during which
they had to report on research articles published in the journals.
Professor Wallace also brought in several researchers in topological
semigroups, like Professor David Foulis and apparently Professor
F. M. Sioson.  During the time I was in graduate school, I recall
seminars on orthomodular lattices conducted by Professor Foulis for
graduate students and some faculty.  Professor Wallace conducted a
seminar on topological semigroups and cohomology.  The A. D. Wallace
seminar met on Tuesdays and Thursdays.

	Professor Maxfield was a commanding figure with a handle bar mustache,
standing 6' 6''.  He had a collection of vintage Rolls Royces and also a
stretched Checker limo.  I recall driving to an American Mathematical
Society meeting in Houston, stopping overnight in New Orleans, in the
Checker limousine with Dr. Maxfield and a group of graduate students.
In 1967, Professor Maxfield left Gainesville to become Chairman at
Kansas State.  He took several faculty members and a group of graduate
students with him.  The question arose as to how all of these vintage
cars were to be transported to Kansas.  A graduate student was charged
with driving one of these vehicles, but it overheated and broke down
as near as Lake City, and may have had to finish the trip being
transported on a truck.''

I asked Maxfield during our telephone conversation about the Checker limousine,and he replied that it was important to get the graduate students into a research atmosphere, attending mathematical meetings. He had encouraged them by taking them himself to the meetings in one of his vintage cars!

Al Bednarek told me the following Foulis story. Foulis tired of being eternally asked what orthomodular lattices are good for. He purchased a Cadillac and had his photograph taken with this vehicle, which he explained was purchased with the aid of grant money obtained to carry out his research program on orthomodular lattices!

A second alumnae, Professor Jane Maxwell Day, was kindly sent me the following e-mail recollections of her graduate students days on August 20, 1994:

	``Yes I was at UF during the Wallace years.  My thesis advisor was Wayman
Strother, himself a Wallace PhD from Tulane.  I think Wayman came to UF in 
1961, recruited by the new chairman John Maxfield.   Wayman taught a prove-it-
yourself topology course, using Wallace's `AT I' Notes, and I thought it 
was wonderful!  I believe that Wayman was primarily responsible for 
wooing Wallace away from Tulane.  The story I heard was that he and Maxfield
developed a strategy to offer Wallace the opportunity to build another great 
math dept.;  he insisted on a $25,000 salary, which was about 3x what most UF
profs made then; so they had to convince the university and legislators that 
Wallace would bring in so much NSF research money that UF would still come
out ahead.  And it all worked.  Wayman referred to Wallace as `ADWA,' other
semigroupers called him `the great white father' (his hair was very white),
and everyone held him in awe.  He always wore a silk suit with a rosebud
in the lapel---not typical mathematician attire!---but on him it looked just right.  

	We had many eastern European visitors after ADW came (in 63 I think).
I was fortunate enough to be invited by Wallace to be his `assistant' for two 
years, which meant taking notes in his course on semigroups and writing those 
up; and doing other things like helping visitors find housing, looking up 
early papers on topology, etc.

	After I got my PhD in 64, Wallace invited me to do some research with him 
and I also got to teach some interesting stuff like Dimension Theory
from Hurewicz and Wallman.  I remember those as being great years.  I had
never really intended to `be' anything, and only started grad school to
kill some time before having a family.  But Strother and Wallace were
excellent teachers and encouraged me greatly.  They both had gifted 
daughters, and great respect for Mary Ellen Rudin; perhaps those 
things explain their special willingness to encourage women in mathematics.   
I realized later they were way ahead of their time in that.''

In connection with my writing an article about Professor Day for the Walker Hall Review, I requested a copy of her vita, and so came to learn that she had co-authored a paper with K. Kuratowski, ``On the nonexistence of a continuous selector for arcs lying in the plane,'' Indag. Math. 28 (1966), pp. 131--134. I inquired about how this article came into being and received a follow-up e-mail message from Day on August 24, 1994:

``Hello Prof. Ehrlich:

Yes, `AT I' was the name of the year-long `prove it yourself' algebraic 
topology course which Wallace developed at Tulane and transported to UF.  
The first half was point set topology and the second half was the kind of
cohomology Wallace liked, because it did not require the spaces to have
any special structure (no triangularization or differentiable structure 
needed).  I think people called it ``Alexander-Kolmogorov-??
cohomology.''  Kermit Sigmon may remember the moniker better.  
The AT I notes contained definitions and statements of theorems, and each
student in the class was supposed to prove all the theorems.  There was 
a rigid ethic associated with AT  ---each student worked alone, 
and did not consult books.  Also, if no one had a proof of the next theorem 
when the class met next, class was dismissed.  If one or more students had 
proofs, the instructor chose one person to put it on the board and then 
the class critiqued it.  

I think Wallace used AT I to measure students' talent, as well as 
preparing them to work on semigroups---certain theorems in those notes
were especially hard, and he knew how long it had taken earlier students 
to get the proofs, and the kind of proofs they had constructed.  So he 
could compare new students to ones he had taught before.  

Although Wallace's PhD was with G.T. Whyburn at U Va. and Whyburn was
a student of R.L. Moore, as far as I know, Wallace never taught any 
course exactly the way Moore did.  (As I have heard about Moore, he
provided no definitions or theorems---students had to develop it all.)
Yes, the Kuratowski with whom I wrote a very short paper is the famous
topologist.  He stayed in Gainesville several months, during the fall
of 1964 I think, and was a really charming man.  He asked a question
in one of his lectures and I answered it with a counterexample, so 
that's how our joint paper occurred.  The first time he lectured I
thought `This is going to be so boring,' because he wrote in a very careful 
and deliberate manner on the chalkboard, and he began with the definition
of a topology, which by then I was sure I knew as well as anyone in the
world!  So I sort of mentally dozed off, only to come to a few minutes later
realizing he was writing something on the board I had never seen 
before and suddenly it seemed he was writing much too fast!  I did not 
underestimate him again.  

C.B. Smith was my Masters thesis advisor.  I had taken several courses 
from him and thought he was an excellent teacher.  He collected homework
every day and graded it himself.  He was the first college math instructor 
I'd  had who did that, and the first one for whom I worked regularly!  
I am still very appreciative of the discipline he instilled in me, and 
my teaching style has always included collecting some HW regularly and 
grading it myself.  I didn't like complex analysis very much however,
and had decided to quit after my MS but then I discovered topology. 

I think Wayman Strother still lives in south Florida; if you are going to 
write about the Wallace years, you definitely should talk with him.  I
probably have his address at home, and will try to remember to bring it
to school and send to you.''

Concerning European connections, let us mention another example, important to the Department. In 1961, A. D. Wallace gave an address at an International Symposium on Topology held in Prague and thus came to lecture at European universities in the following cities during 1960--61: Vienna, Austria; Bratislava, Czechoslovakia; Turingen, Germany; Budapest, Hungary; Krakow, Poznan, and Warsaw, Poland; Bucarest, Roumania; and Belgrad and Zagreb, Yugoslavia. Professor Zoran Pop-stojanovic was Wallace's host during his visit to the University of Zagreb in 1961; in 1965 Zoran came to the University of Florida as Visiting Assistant Professor, and would serve as Associate Chair from 1972--1986 during the Bednarek Chairmanship. (The more refined structure of Associate Chair for Undergraduate Studies, and Associate Chair for Graduate Studies was not put into place until 1984, when Professor Bruce Edwards would become the first Associate Chair for Undergraduate Studies.)

We began our story with the goings on in Lake City in 1903--1904, and have worked up to the 1970's. It is tempting to quote the final paragraph from Professor Samuel Proctor's 1958 dissertation, [13], The University of Florida: It's Early Years, 1853--1906, at this juncture; here Proctor is describing based on newspaper reports the inaugural ceremonies held for the opening in Gainesville on September 27, 1906:

	``The audience, although wearied by the lengthy program, applauded the
speeches.  According to the newspaper account, `all of Gainesville, male
and female, from the wee bit of a youngster to those who were so advanced
in age that they could not walk and were compelled to take other means of
conveyance, were present ... and a happy crowd it was, too. The babies
laughed and cooed as if they understood the situation, the faces of the 
elder ones were wreathed with smiles of satisfaction, the speakers seemed
at the best and most enthusiastic mood, and in all it was an occasion the
likes of which was never before witnessed in this city.'

The University's most difficult years were now over, and, although disappointments and discouragements still would be experienced and obstacles would still remain to be surmounted, the pathway to the building of a real University, with all of its challenges and opportunities, lay ahead.''

We started with essentially one man departments under Karl Schmidt and Herbert Keppel prior to World War I, then saw some expansion with the coming of Thomas Simpson to Gainesville after Keppel died of the Spanish influenza in October 1918, especially during the brief prosperity of the 1920's.

This brought another pioneering faculty member to the University, Franklin Kokomoor. Simpson and Kokomooor would labor together in the academic vineyards until 1951 when Simpson retired, only to keep on teaching elsewhere almost until his death. Together they worked to see the University through the trying days of World War II. Kokomoor then led us up until 1960, over thirty years after he first set foot in Gainesville. John Maxfield, coming from California as the first outside chairman in over 40 years, participated in national trends (with Florida, of course, taking these up five or so years later than the Northern institutions) in decreasing emphasis on service teaching as our primary mission, reduction in teaching loads, and an increased emphasis on research.

As we have seen in this chapter, and as many current faculty who were here during those times have agreed, the appointment of A. D. Wallace in 1963, who would serve as the first Graduate Research Professor in the department after 1969, was the bridge to producing the department which I joined in 1987. The simultaneous appointment of Al Bednarek in 1963, provided us with the leader who would take us from 1969 up into the mid eighties. Other faculty, like Lou Block, Beverly Brechner, Philip Bacon, Thomas Bowman, Jim Brooks, Douglas Cenzer, Nicolae Dinculeanu, David Drake, Chat Ho, Rudolph Kalman, Jed Keesling, Jean Larson, Jorge Martinez, Charles Nelson, Vasile-Mihai Popov, Zoran Pop-Stojanovic, Murali Rao, Gerhard Ritter, Stephen Saxon, Rick and Jane Smith, Chris Stark, John Thompson, Arun Varma, Andrew Vince, Helmut Voelklein, Neil White, and David Wilson, many of whom I would meet while on an interview trip to the University of Florida during 4 days of December, 1986, would be recruited to the department during the Chairmanships of Maxfield, Wallace, and Bednarek.

We will leave it to a future writer to seek out the many colorful stories stemming from Graduate Research Professor Stanislaw Ulam's winter visits to Gainesville during the Bednarek Chairmanship.


  1. Marsden, George, The Soul of the American University, Oxford University Press, 1994.
  2. Duren, William, ``The most urgent problem for the mathematics profession,'' Notices of the American Mathematical Society, Vol. 41, No. 6 (1995), p. 582.
  3. Paul Halmos, I want to be a mathematician: an automathography, Springer Verlag, New York, 1985.
  4. Proctor, Samuel and Langley, Wright, Gator history; a pictorial history of the University of Florida, South Star Publishing Co., Gainesville, Florida, 1986.
  5. Selfridge, Ralph and Maxfield, John, A table of incomplete elliptic integrals of the third kind, Dover Publications, New York, 1958.
  6. Maxfield, John; Maxfield, Margaret S.; Sadler, S. Gould, Contemporary mathematics for general education: algebra, Allyn and Bacon, Boston, 1963.
  7. Maxfield, John and Maxfield, Margaret, Abstract algebra and solutions by radicals, W. B. Saunders Company, Philadelphia, 1971.
  8. Niven, Ivan, The threadbare thirties, a century of mathematics in America, ed., P. Duren, R. Askey, U. Merzbach, Part I, American Mathematical Society History of Mathematics, Vol 1 (1988), pp. 209--229.
  9. Florida Section Invited Addresses, 1986, Mathematical Association of America, ed., Don Hill.
  10. Koch, Robert, ``A theorem a day, a tribute to Alexander Doniphan Wallace 1906--1986,'' invited address, M.A.A. Florida Section, ed., Don Hill, 1986, pp.69--81.
  11. Bednarek, Alexander, ``Alexander Doniphan Wallace, The Florida Years, 1963--1973,'' invited address, M.A.A. Florida Section, ed., Don Hill, 1986, pp. 82--89.
  12. Lin, You-feng, ``A Theorem of Wallace,'' invited address, M.A.A. Florida Section, ed., Don Hill, 1986, pp. 90--92.
  13. Proctor, Samuel, ``The University of Florida, it's early years, 1853--1906,'' Ph.D. Thesis, University of Florida, 1958.

Appendix A

Not With A Hatchet

Here is the text of the evening address delivered by Graduate Research Professor Alexander Doniphan Wallace at the initiation banquet of the University of Florida Chapter of the Phi Beta Kappa honorary society, on December 2, 1971.

	``My text for this evening is taken from the consecration sermon for
two archbishops and ten bishops preached by the Right Reverend Jeremy Taylor,
Bishop of Down and Connor, at St. Patrick's Cathedral Church, Dublin, in 1660.

	Those not entirely familiar with the tortuous ramifications of the
religious history of that time might wish to know that the good bishop
was an Anglican, of the Church of England.  Charles II had returned from
exile in the Netherlands, and since the Cromwellian Puritans scorned
with most pious indignation the transmontane trappings of the Anglican
Church---as do the relevantists of today---there was a
great dearth of religious overseers.  Hence the large number raised to
episcopal rank at that time.

	Jeremy Taylor was forthright with his advice to the new Shepherds of
Souls, and a few lines from his sermon, which I paraphrase in part,
serve to indicate his thinking.

`Preach often' ---a twelve-hour preaching load?--- 

`and pray continually; let your disciplines be with charity, and your
censures slow; let not excommunication pass for trifles, and DRIVE NOT

	He continues that God will call to a severe account the idle shepherd.

	`Now, think you, will his anger burn, when he shall see so many goats
standing to his left hand, and so few sheep at his right hand, and
upon inquiry shall find that his ministering shepherds were wolves in
sheep's clothing?'

	He speaks next of the ill example and pernicious doctrine of the false
shepherd, his care for money, and his careless treatment of the flock
letting `so many souls perish, while, if they had been carefully and tenderly,
wisely and conscientiously handled, might have shined as bright angels.'

	It is here, tonight, that it is our pleasant obligation to pay homage to those
who have `shined as bright angels.'  And it is to them that I address words of
commendation for excellence, those who, in this academic democracy of
opportunity, have by their effort placed themselves in the aristocracy
of achievement. As a modern recension of Leviticus might have it,

		`Let us now praise famous men and women.'

	If we are to extol their accomplishments, we must ask what it is they
have accomplished, what they were then and what they are now, what
it was that they brought with them, what help aided them along the way 
and what hindrance there was on their path to excellence.  But this is
neither the be-all nor the end-all upon their bank and shoal of life, and we
must not jump their life to come.

	They---our bright angels---entered as timid freshmen
(if there are timid freshmen in these days) upon a veritable chaos of
well-intentioned confusion, beset on every hand with rules,
regulations, prerequisites, and sound, if contradictory, advice from
both their coevals and their learned seniors alike.

	They were told---if they came the UC [ed., University
College, or Lower Division] way---of the great dangers of
departmentalization, and of professionalism, though in all probability
they were not warned of the equal danger of cross-sterilization, nor
of the invalid method of solving difficult problems in one discipline
by relying upon the formulation of a dubious truth in some other
discipline. They were subjected to bits-and-pieces education, what I
may term jig-saw puzzle education.  But they learned to fit the small
multi-colored, queerly-cut pieces into a pattern that gave them a
picture sufficiently clear to at least surmount with some honor our
system of academic book-keeping.

	Perhaps it is unimportant what constituted the propadeutic barriers
over which they climbed, for, whether with pleasure or with pain, their
efforts met with success. If their brows were somewhat bloody, they had not,
at least, been seriously maimed by the academic hatchet.  

	Among the greatest thinkers of this century was Alfred North
Whitehead.  He was---for a while---a mathematician and
logician of great distinction, and he was always an eminent
philosopher.  I wish to do no evil to his memory when I say that he
was a great educator, for to call a person an `educator' now has a
perjorative connotation.

	Said Whitehead, and I paraphrase: A merely well-informed man is
the most useless bore on God's earth.  What we must have are people
who possess both culture and expert knowledge in some special direction.
Their expert knowledge will give them the ground to start from, and their
culture will lead as deep as philosophy and as high as art.

	And now our bright angels.  They leave the domain of generosity (but
not abstraction) and venture into an upper-division college, where
specialization (but still not abstraction) is their share.  University
College was their bouillabaisse, and their olla podrida, but now they
must eat the strong meat of specialization, prepared for their delectation
by chefs of great expertise.

	Now a person might think that the transition from UC to an upper
division college would be smooth and relatively comfortable, for these
are parts of the same university separated by no great distance, the
one from the other. Perhaps there is frequent consultation and regular
collaboration, meetings of faculties to insure that the curricula mesh
and that the programs integrate toward a common end.  Perhaps this is
the case, but I have found little evidence to confirm it, and when I once
raised the question at a Senate meeting the response was a sputtering burst
of indignation, presumably at this daring attack upon an autonomous body.
But perhaps the transition {\sc is} easily made after all, so let it go
at that. At any rate it was no great obstacle to our bright angels.

	Now the pleomorphy of an upper division college is considerable,
and particularly so is A and S, where one ranges from the A of
Anthropology to the Z of Zoology, by way of Chinese, French, Germanics,
Slavics and Swahili, no doubt old French, old Italian, and possibly
Old Outlandish.  In any event each of our bright cherubim---then only
in the diaconate---attached himself to some department on the way to
becoming an expert, to the extent that two years would permit.

	We set them the task, and they accomplished it with excellence
to spare, and there is not much more that one could ask of them.  
But there is, I think, something that must be said of our share
in this educational operation.  We have erred and strayed from the
way of the good shepherd in at least two respects, as I see these
things.  At the risk of arousing the ire of my colleagues I should
like to go briefly into them.  It goes without saying that I have
by no means matched educational philosophies with all of my colleagues,
and I hope very much that my views are shared by many of them.

	For one thing we have tried very hard to teach our bright angels,
and our obsession with this teaching business has got sadly in their
way of learning. For another thing, we have not disabused our students
of the notion that they must be taught.  We have left them with the
fallacy of the schools, that they can be taught, that they ought to
be taught, and that they will be taught, come hell and high-water.

	One must presume that this is primarily an educational institution,
and that the principal reason for students being here is to learn, and
to learn to do.  We all know this, but perhaps our love of teaching
surpasses, on some occasions, our love of learning.  Perhaps we try
too hard to earn the munificent stipends which the legislature appropriates
to us.

   In these days we must be evaluated, and numbers must be attached to
us via the arcane process of statistics, so perhaps we are trying too
hard to get good grades on our evaluation sheets.

  Whatever may be so, it seems to me that we attempt the
impossible---we try to make the students learn by trying to
teach them, and failure is an inevitable outcome.  The students
succeed despite us.

	Let me turn to an equally important, but different, aspect of our
educational process.

	A university catalog is most likely to be an accumulation of dusty
rules, regulations, programs, requirements, prerequisites, and
whatnots from a long forgotten past.  I should like to see the great
bulk of this swept away, and replaced by something more reasonable,
and more pertinent to the educational process. There should be greater
freedom of choice, including the freedom to make mistakes. The distributional
requirements---born of academic protectionism and misplaced belief
in professorial wisdom---ought to be abolished. If in this
matter I am an iconoclast---a breaker of idols---then
I must say that those with whom I am in disagreement are
iconodules---slaves of idols.

	Let the student take whatever he will, but in accordance with Whitehead's
dicta there must be a major and, in order that there not be unfair
competition in the academic arena, half of the courses over and above
the major must be in the upper division.  A short paragraph will
encompass all college requirements.  In this matter I do not speak for my
Department, but I should vote---if I had the opportunity to vote---to at once
strike down the pernicious demand that every student take
mathematics.  It would be improper to say what another upper division
college ought to do, so that here there is only the A and S in

	There is one additional matter that can be raised in this context,
though it might at first seem out of place in this august assemblage,
and that is the system of academic book-keeping.  Now this keeping of
grades, this attaching numbers to people is anathema.  It is a necessary
evil, but one under which we all squirm like a congeries of eels confined
to a small aquarium.

	It appears to me that it might be simplified, to some benefit to all
of us. I suggest that the present system be replaced by one with only three
grades---Honors, Pass and Fail.  Honors degrees and pass
degrees have held sway in the British universities for several
centuries, so that there is little question but that it might also be
suitable here.  It has built into it the pass-fail option. It has also
the possibility of high reward for those whose interest is
sufficiently great. But enough of this for now.

	It might be thought, indeed with some truth, that I have concerned
myself too much with telling my learned colleagues how to do their business,
how to run their shops.  But among our bright angels there are surely
some who will one day be even brighter archangels, and who will sit in the
seats of the mighty. From that eminence they may look backward, as
even angels do, upon these notions.

	As a mathematician it is presumed, I suppose, that I will say something
about mathematics.  Nothing technical, nothing to chill the joyous nature
of this occasion, but only a few, almost casual but nevertheless penetrating,
remarks on an ancient and honorable discipline.  Whether it is my
pleasure and your opportunity, or the other way around, let me say a

	Some two thousand three hundred years ago a professor at the University of 
Alexandria, in Egypt, published an elementary textbook.  He was not titled
`professor', for the word did not then exist, nor was his institution a
`university', and we think today that it was more like a research institute than a
university.  His name was Euclid, and today we call his textbook 
Elements of Plane Geometry.  It is surely the most popular textbook ever
to have been written, for after the passage of more than two millennia we use
it still in one or another form.  Had it been published by the same firm over
all of these years it is clear that the firm would now surpass in wealth a
thousand General Motors Corporations. Now the test of greatness is---to put
it bluntly---survival. And Euclid's book has survived, and is in continuous
daily use.

	It is customary in the circles in which I move to denigrate writers of
merely elementary textbooks. And I must say, in Euclid's behalf, that there
is a great deal of his book that we do not teach, what one would recognize as
`new research' of that era.  Essentially nothing is known of Euclid the man,
and one can---and some do---debate Euclid's authorship of `Euclid's Elements'
in much the same way that Shakespeare's authorship of Shakespeare's plays is
debated---but of course only by amateur cranks.

	Euclid was certainly an archangel, but perhaps more of an archaeopteryx.

	In the two thousand years that followed Euclid much mathematics was
done---created, if you will---trigonometry and algebra.  There were many
bright angels who, no doubt, plucked quills from their wings to make their
writing tools. But the entirety of these years must pass before the heavenly
host was augmented by an angel of Euclid's worth magnitude, Issac Newton.

	Here indeed was genius.  In that Annus Mirabilis---the year of miracles---
1666, or close thereto, this giant who stood upon the shoulders of giants---
as he put it---discerned for the first time the workings of the heavens.  As
Alexander Pope put it---God said let Newton be, and all was light.  And Laplace 
said, with some envy, 

	`It is given to but one man to discover the system of the universe.'

	What is truly remarkable about this is that Newton not only discovered 
the system of the universe but invented the mathematics necessary thereto, 
without which its explication was impossible, and its theorems unprovable.
His great book, written much later, he called The Mathematical
Principles of Natural Philosophy

	From an inchoate pool of information and misinformation, gathered over
the centuries by accretion and accumulation, replete with ambiguities and
otiose moities, Newton constructed the first of the great scientific
paradigms. So simple as now to appear simplistic, so banausic as to
provide a road-map to the moon, a paralipsic but apodictic code,
containing three commandments only, whereby the physical universe was
ruled.  From this trinity of dicta there came a veritable
constellation of consequences, with scope and depth beyond even the
imagination of Newton's predecessors, and his three commandments were
to remain the rubric for physical science into this present century.
But without the differential and integral calculus, which Newton
invented, there would have been no language in which this could have
been written, no formulary for the preservation of its observations,
and no apparatus for its predictions.

   If Euclid alone has looked upon beauty bare then Newton, that
watcher of the skies, stood first upon the peak in Darien and looked
into the open face of all the heavens. 

	But, over and above all of this, Newton was a superb experimenter
and a man of many practical qualities.  As Master of the Mint he was
in charge of British coinage, perhaps the equivalent of today's treasurer
of the United States. Earlier he had taken the leadership of Cambridge
against an appointment which James II wished to make.  Nevertheless,
in common with all of us, Newton had his failures. He turned to theology,
on which he wrote volumes---but to no avail. Theology has passed him by
and even his heresies are forgotten.

	What is this mathematics that most of us dislike so passionately,
and avoid so diligently, however much we may marvel at those who
practice it well?

	It is an odd discipline which has its roots in far antiquity and yet
continually plagues us here and now.  It is as old as yesterday and as
new as tomorrow. When the archaeologist digs into the ruins of some
forgotten culture and finds, incised in metal or punched into clay,
some relict of intelligence, there is almost certain to be some system
of numeration, and this in general is the most quickly read of all
symbols that are found.  I know of only one exception to this; in
as-yet undeciphered Etruscan, although the words for numerals are
known, it is not known what word stands for what numeral.

	One may make a conjectural definition of mathematics, or time of
entrance of mathematics into civilization, in saying that mathematics
arrived when it was first known that the `two' in `two men' and the
`two' in `two women' were the same `two.' To all of us this is a
triviality, but there must have been a time when this triviality was
still in obscurity.  One may conclude that mathematics is, among very
many other things, an abstraction.

	In every civilization of the present or the past some mathematics
plays a fundamental role.  It would appear that this is a subject that
was many times discovered in many civilizations, the one quite
independent of the other.  For the Mayans used, among other things, a
numeration to the base 20, and the Babylonians one to the base 60, but
in Minoan culture the base ten appears to have been used. So
mathematics has about it a universality.

	Is mathematics an abstract universal, or a universal abstraction?

	There is another sort of universality about mathematics, which can
most easily be apprehended in this fashion: More people on this campus
use mathematics---in some form or other---than any
other subject taught here, with one exception of our common English
language.  As has just been observed, mathematics is inter-cultural,
in the sense that it is common to all sufficiently advanced cultures.
But its intra-culturality is decided, for no discipline can today term
itself a science without the use of some mathematics.  Of course not
always the same part of mathematics, for partial differential
equations appear rarely in biology, and systems analysis and matric
algebra are not regularly used in organic chemistry.  As a somewhat
unusual example, there appeared some 15 years ago a weighty tome in
German entitled Mathematical Jurisprudence, and prior to that by
25 years, the mathematician Andre Weil reduced to mathematical form
the so-called marriage tables, which state the permissible
degrees of consanguinity for marriage.  These are things beloved of
anthropologists, and useful in their investigations of primitive

	As a final example of intra-culturality, there is the problem of
Geoffrey Chaucer, the English poet of the late 14th century, or
perhaps one might say, the problem of `the Geoffrey Chaucers.' In
addition to the practice of poetry Chaucer appears to have been a
civil servant who moved in diplomatic circles, and who had an
important part to play in the wool-trade.  In these activities, in
addition to his literary work, he must have written many papers, or at
least have signed his name many times. Yet there seems not to exist a
single specimen of his hand-writing, or at least such was the case
some 15 years ago.

	Now it is supposed that Chaucer was somewhat of an astronomer, and
had indeed written a book, or long paper, on the subject. Such a MS
was found which might well have been written in Chaucer's time.  This
was subjected to linguistic and statistical analysis and the conclusion
was that the probability was very high that it was in the Chaucerian
rubric. The reaction of the critical experts of that period of English
literature was as might have expected---it ranged from outward annoyance
of such nonsense, through total indifference, to mild acceptance.

	One may conclude that mathematics is abstract and universal.
Strangely, if this has been given no thought, one may reason that
intra-culturality implies abstraction. For how could some very concrete
subject be so widely used in so many varying disciplines? Otherwise, it
is its abstractness that makes mathematics so useful to so many.

	There is about mathematics a mystique---perhaps some would say
a hidden mystery---of a unique character, for which there
appears to be no word, in any language, adequate for its description.
One might perhaps use `necessity', but this has not the desired
connotation.  What is meant can probably best be indicated by quoting
from Einstein and Wigner.

	There is no need to say anything at all about Einstein, he is too
familiar. In a Rhodes Lecture which he gave in the thirties concerning
physical principles he said this: I am convinced that we can discover by
purely mathematical constructions the concepts and the laws connecting
them with each other, which furnish the key to the understanding of natural
phenomena.  Experience may suggest the appropriate mathematical concepts,
but certainly they cannot be deduced from experience. Experience remains,
of course, the sole criterion of the physical utility of a mathematical
construction.  But the creative principle resides in mathematics.

	As to Wigner, he is the recipient of a Nobel Prize and a professor of
physics at Princeton.  I quote from his paper `The Unreasonable
Effectiveness of Mathematics in the Natural Sciences'---

	`The first point is that the enormous usefulness of mathematics in
the natural sciences is something bordering on the mysterious, and there
is no rational explanation for it. ...  It is difficult to avoid the
impression that a miracle confronts us here ....'

	The role of mathematics in the biological, social and humanistic
sciences is not yet known, for these disciplines have not yet found
their Euclids and their Newtons. Although mathematics is much used in
economics, for example, that useful and essential collaboration between
these two disciplines seems not to have surfaced yet.  Quite possibly
the fault lies in mathematics, and it is by no means certain that
mathematicians have yet invented the sort of mathematics necessary for the
explication of economics.

	There is a general misconception that mathematics is a science,
and nothing could be more remote from the truth.  If one uses the word
`science' in its very old meaning of a coherent and organized body of
knowledge, then of course mathematics is a science and so is literary
criticism, history, and so on. But mathematicians do not experiment with,
nor do they make observations of natural phenomena.  Both musicology and
sociology are more scientific than mathematics.  Harmony, as a
subdiscipline of music, is a codification of the common practice of
vertical writing of musicians in the 18th and 19th centuries.  It is
the collected and systematized deductions gathered by observing the
practice of composers. Of course, every composer in his time is an
experimentalist. Perhaps his manner of writing will some day be
incorporated in the great musical paradigm, and become a part of the
common usage of musicians.

	The mathematician experiments in much the same manner as the composer,
but the musician is much closer to reality, for one can neither hear
nor see mathematics, it is all a figment of a fertile imagination, it
has not the verisimilitude of reality. It would be wrong to suppose
that mathematics came ex nihilo, out of nothing at all.  But in a very
certain sense it sprang from the imagination of man, as Minerva did
from the forehead of Jove.

	Perhaps, if mathematics is not a natural science, it is an
unnatural science. Whatever may be its numinous role in the body of
all thoughts and things, there is constation of its panoptic

	If a definition of mathematics cannot be approached in a positive
fashion, then perhaps one should take the way of the NAY-SAYER (who is
not the contrapositive of the yes-man) who sought to say what things
were by saying what they were not.  The doctrine of apophasy, of the
nay-sayer, was a part of the eastern mystical theosophy, codified by
Origen of Alexandria, who followed Euclid by some five centuries.  It
was cultivated later by others, and much of its development has been
attributed to Saint Dionysius the Areopagite.  Its influence on Saint Thomas
Aquinas, in his Summa Theologica, has been emphasized. But the
orthodoxy of the apophasist has gone the way of Newton's heterodoxy.
Were I a philosopher instead of a mathematician, perhaps I could make
something of the apophtic way.  For mathematicians, as for apophasy,
perhaps the only comprehensible thing is incomprehensibility.  All of
this is very close to nonsense, the vertiginous abyss of
transcendentalism. Georg Cantor, the inventor of sets and functions,
those mysterious notions that befuddle parents attempting to do their
children's homework for them, spent more than the latter third of his
life confined to institutions for the treatment of mental

	Genius is sometimes close to madness, and sense to nonsense.  Some
of the most pleasant nonsense was written by a mathematician.  He was
not a great mathematician, or even a good mathematician, and in fact
the most that can be said for him was that he was a mathematical

	He was a lecturer in mathematics at Christ Church College, in Oxford
University, and the author of at least one rather poor book on
mathematics, which was dedicated to Queen Victoria at her
request. This was the Reverend Charles Lutwige Dodgson. His literary
efforts were phenomenal, using `literary' in its broadest meaning. At
his death there survived his `letter-book'---a compilation of
extracts of the letters he wrote and received, with the gigantic total
of almost 100,000 entries. His published works, excluding mathematics,
run to some 1200 printed pages.  He was a person of great piety, and
social bravery, and vulgarity was to him the very worst of vices. He
was a gentle man, in every meaning of this word.

	Under the fictitious name Lewis Carroll, he wrote the most pleasant
nonsense ever penned in the English language, Alice in Wonderland, 
Through the Looking Glass, and much else.  His utterly fantastic
imagination can best be brought forward in some of his lesser-known

			He thought he saw a rattlesnake
			That questioned him in Greek;
			He looked again, and found it was 
			the middle of next week. 
			'The one thing I regret,' he said, 
			'Is that it cannot speak.'

	But his conclusions from irrelevant hypotheses were sometimes

			He thought he saw a kangaroo 
			That worked a coffee-mill; 
			He looked again and found that it was 
			A vegetable-pill. 
			'Were I to swallow this,' he said,
			'I should be very ill.'

   Lewis Carroll was certainly not an archangel, at least mathematically, but
it is equally as sure that he was an angel, if only a very small one.

	Mathematicians come in all shapes and sizes, and from all walks of life. Let
me mention a few names, all in the archangelic hierocracy, with a brief
	Mathematicians are after all, human beings.

	So much for the casual, if penetrating, remarks concerning my own

	And now back to our bright cherubim and seraphim, and no less,
to those whose support their sojourn in this grove of academe was
made possible, their parents. To these we must express appreciation
that they found this university a fitting place, a suitable depository
for their hopes for their children.  In this day of fluctuating
interest rates, depression and recession, we are encouraged that
their investment for the future of their progeny was a safe and sound
one, for a good education rarely depreciates, whatever the state of
the market.  And to those who accompany our bright angels---their
uncles and their cousins, whom they reckon by the dozens, and their
aunts---our pleased acknowledgment of their presence here.

	In this event I stand in surrogate to Polonius, that sentitious
father of Ophelia in Shakespeare's Hamlet.  You will recall his pious
platitudes, uttered in stained-glass attitudes, that flow of verbal
morality and sage council, given to direct conduct and opinion of
others.  In my role as non-teacher I must forgo this. In its place,
and I hope more welcome, the very sincere congratulations of all
of us to the initiates of this evening.

	It is somewhat of a mystery as to why those in charge of this
occasion might have thought that a mathematician would be an
appropriate speaker. Whatever may have been their reasoning
---or their unreasoning---my most grateful thanks to the officers
of the chapter, and in particular to Dr. Spivey, for the opportunity
of making public some of my views on education. There are also others.

	At such times as this, occasions of tedious oratory, I am reminded
of Old Father William and the questioning youth.  I trust
that my dear wife will forgive the allusion.

	`You are old,' said the youth, `and your jaws are too weak 
	For anything tougher than suet: 
	Yet you finish the goose with the bones and the beak---
	Pray how do you manage to do it?' 
	`In my youth,' said his father, `I took to the law, 
	And argued each case with my wife; 
	And the muscular strength which it gave to my jaw 
    Has lasted the rest of my life.'

	For your kindness and courtesy in listening so patiently to this septic 
torrent of quotations, my boundless gratitude.

Thank you, very much.''

Appendix B

The Center for Applied Mathematics (CAM)

As I write, one of the strengths of the University of Florida is the existence of about 200 centers and institutes on campus. One of these, historically connected with the Department of Mathematics and with some of the personalities encountered in this chapter, is the Center for Applied Mathematics. Recently, Professor David Wilson of our department (with the assistance of Professor Zoran Pop-stojanovic on historical matters) wrote up a document for the departmental web page which gives the history of this center, and with Wilson's permission, we have reproduced the relevant portions of this write-up below:

  ``The Center for Applied Mathematics (CAM) was formed in 1974 through a
    cooperative effort of Professors A. R. Bednarek and Knox
    Millsaps. Letters
    of support for the formation of the center were provided by a number
    of prominent University of Florida individuals including E. T. York,
    Linton E. Grinter, and Harry Sisler. Dean Grinter wrote an extensive
    white paper delineating the structure, goals, and aspirations of the center. In
    addition, in a letter to Dean Harold Hanson he made the following remarks.
    `My thought, expressed in the white paper attached, is that an
     opportunity exists to train applied mathematicians here at several
     levels by using courtesy appointments of qualified faculty to a
     Center for Applied Mathematics. This Center would require a
     half-time Program Director and a Coordinating Committee to
     establish degree standards. Hence costs would be minimal.
     Nevertheless, the effect in the South, and therefore upon
     Washington sponsors, might be quite significant because comparable
     degrees seem limited to Rice, Georgia Tech and North Carolina

Chancellor Robert Mautz set in motion the formal mechanism for the creation of the center in a letter dated 6 February 1974, when he wrote:

    `I note that establishment of the proposed interdisciplinary
     Center for Applied Mathematics will aid in the training of students at
     both the undergraduate and graduate levels in various aspects of
     applied mathematics. While I encourage the interdisciplinary
     approach and optimization of campus resources in mathematics which
     this center may engender, establishment of the Center should not
     be interpreted as encouragement to plan any additional degree
     programs in the mathematical sciences at this time.

     The University of Florida is hereby authorized to proceed with the
     establishment of an interdisciplinary Center for Applied
     Mathematics. No further action is necessary.'

The Center was started at The University of Florida because of the presence of a strong group of internationally recognized applied mathematicians including the late Stan Ulam, late Karl Pohlhausen, M. Popov, and M. Longuet-Higgins. Soon this impressive group was joined by another internationally recognized authority, the late L. Cesari, who was instrumental in organizing the First Symposium on Dynamical Systems, held at UF during 24--26 March 1976. The funding for this symposium came from the State of Florida's Quality Improvement Program. Five years later, during 25--28 February 1981, the CAM held the second Symposium on Dynamical Systems (under the same source of funding as the first). The central theme of the symposium was the relation of dynamical systems to current research on ordinary and functional differential equations, partial differential equations, stability theory, and optimal control. The Proceedings of the symposium was published by Academic Press. Also, during 1981 the CAM organized a Seminar on Stochastic Processes with funding from the Division of Sponsored Research. The proceedings from this conference were published by Birkh user. The CAM organized three more Seminars on Stochastic Processes, the last held in 1995. Funding for all these seminars came from the Division of Sponsored Research and the College of Liberal Arts and Sciences. The Center also sponsored the Sir Jeffrey Taylor memorial lecture series, which featured many distinguished speakers including Stan Ulam, Mark Kac, Felix Browder, G. Carrier, and M. Longuet-Higgins.

Administrative Structure

In his letter to Vice President Bryan dated 17 January 1974, Dean Harry Sisler proposed the following structure for the Center.

The original council consisted of Associate Vice President Robert A. Bryan, Dean Wayne H. Chen, Dean Harry Sisler, and Dean C. A. VanderWerf. The Council has now been replaced by Professor Karen Holbrook, Vice President for Research and Graduate Education. The original External Scientific Advisory Board consisted of J. P. LaSalle, C. C. Lin, J. B. Rosser, G. C. Rota, and S. Ulam. The original administrative structure consisted of Co-Directors A. R. Bednarek and Knox Millsaps. The original faculty in the Center included individuals from the following academic disciplines.

As I am writing in 1996, this institution is seeing a renewal under the directorship of Ulrich Kurzweg from Aerospace Engineering, and Zoran Pop-stojanovic and David Wilson from Mathematics. An new External Advisory Committee has been formed, including Michael Barnsley, John Dennis and Avner Friedman.