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

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

In the late 1800's and early 1900's, it was common for many departments in the less well established colleges and universities of the United States to just have one person with rank of Professor in each department or group of departments. In many cases, Departments of Mathematics consisted just of a single individual with the title of Professor of Mathematics and Astronomy. Even by 1927, our Department still just had one Professor, but now also two Associate Professors, four Assistant Professors and two Instructors. In the 1935 catalogue, the Department now contains three Professors with one listed as Head Professor of Mathematics out of a total of 10 staff members. The title of Chair of the Department seems to have come later, So with this proviso, we list the Past Chairs (or Head Professors) of the Department of Mathematics through the 1970's at the University of Florida together with the institutions where they did their undergraduate and graduate work:

Dr. Karl Schmidt---1905--1908
Ph.D., Marburg University, Germany, 1898
Dr. Herbert Keppel---1908--1918
A.B., Hope College, 1889
Ph.D., Clark University, 1901
[Professor Keppel died in the Spanish influenza epidemic which swept the campus in October, 1918]
Dr. Thomas Marshall Simpson---1918--1951
Dean of the Graduate School, 1939--1951
A.B., Harvard College, 1905; M.A., Wisconsin, 1910; Ph.D., Wisconsin, 1916;
Dr. Franklin Kokomoor---Chair of Department, 1951--1960
Chair of Freshmen Mathematics, 1935--1960; B.S., Valparaiso University, 1915; A.M., University of Michigan, 1924; Ph.D., University of Michigan, 1926;
Dr. John Maxfield---1960--1967
B.S., M.I.T., 1947
M.S., Wisconsin, 1949
Ph.D., University of Oregon, 1951
Dr. Alexander Doniphan Wallace---1967--1969
First Graduate Research Professor in Mathematics, 1969--1973 B.S., University of Virginia, 1935; M.S., University of Virginia, 1936; Ph.D., University of Virginia, 1940;
Dr. Alexander Bednarek---1969--1986, spring 1988
B.S., SUNY at Albany, 1957; M.A., SUNY at Buffalo, 1959; Ph.D., SUNY at Buffalo, 1961;

One notices from this list, particularly, that one person, Dr. Thomas Simpson was Head Professor, then Chair for over thirty years.

When we see the currently advertised fact on our computer screens every time we log on, that the University of Florida dates from 1853, it is important to understand that that is not really the institution here in Gainesville in its current form. Rather in the late 1800's and early 1900's, there came to be eight state institutions, all competing for state funds and all struggling to improve themselves. These institutions together with their dates of founding were as follows:

  1. the East Florida Seminary in Ocala, later moved to Gainesville (1852)
  2. the West Florida Seminary in Tallahassee, later renamed the Florida State College (1857)
  3. the (White) Normal School at DeFuniak Springs (1887)
  4. the South Florida Military College in Bartow (1895)
  5. the Florida Agricultural College in Lake City (1884)
  6. the St. Petersburg Normal and Industrial School (1901)
  7. the Normal School for Negro Students in Tallahassee (1887)
  8. the Florida Agricultural Institute in Osceola County, in Kissimmee (1903).

Now this last institution was never funded by the State Legislature, only authorized to exist, so it can be safely ignored. To confuse matters even further, in 1903, the State Legislature authorized the Agricultural College in Lake City to change its name to the University of Florida, probably with the hope that the quality could be improved to go along with a grander sounding name. A fascinating account of all of these institutions is to be found in Professor Samuel Proctor's dissertation [1] and an unfortunately less detailed account in the more accessible source [2]. All the information about Florida institutions in this introduction and in Chapter 1 is taken from these two sources.

In the late 1800's and early 1900's, various Floridians were proposing and lobbying for the idea that it was neither effective nor efficient to have so many small institutions all struggling along under state funding. Especially by 1904, both President Andrew Sledd of the Lake City Agricultural Institute (by then renamed the University of Florida) and Professor Jere Pound of the East Florida Seminary in Gainesville were both lobbying hard for a coalescing of these institutions into a lot fewer institutions, each man hoping to be the President of one of these new institutions. Also, Professor James Farr, the first Professor of English and German at our current institution, lobbied actively for this change, writing columns anonymously on this issue in newspapers across the state.

The upshot of all of this activity, was that with much political debate on the part of the legislature, the Buckman Act was passed by the legislature and signed into law by Governor Broward on June 5, 1905. Under this bill, all of the white institutions of higher learning in the state of Florida were coalesced into just two institutions, the Florida Female Seminary in Tallahassee, evidently for female students, and the University of Florida, for male students, at a location to be determined by the newly appointed Board of Control. There were two sites which were realistic contenders for the new University of Florida, Gainesville and Lake City. Gainesville put on a tremendous lobbying effort, with Mayor W. R. Thomas himself, one of the prime movers. (So now you know why the two earliest dormitories on campus, Buckman Hall and Thomas Hall received their names). With a great deal of political turmoil, Gainesville won out over Lake City as the permanent home of the University of Florida. In that sense, one could consider the current University of Florida to have stemmed from the merging of the Lake City Agricultural Institute and the East Florida Seminary. However, none of the buildings of the East Florida Seminary became part of our current institution. Proctor notes in [2, p. 25] that

``Because of the inadequate and generally rundown condition of the
East Florida Seminary buildings, the board [of Control] decided to use
the Lake City campus for the 1905--1906 term.''
Rather the main building of the East Florida Seminary became and still is the Epsworth Hall of the downtown Methodist church. Both institutions are, however, represented symbolically in the current school colors, already used in decorating the town and campus during the inaugural ceremonies on September 27, 1906, cf. [2, p. 26] in that the orange came from the East Florida Seminary colors of orange and black, while the blue came from the blue and white colors of the Florida Agricultural College of Lake City.

If we look in the strictest sense, we should study the history of the Mathematics Department from 1905, when the Buckman Act created the current institution and the Board of Control decided to plunk it down permanently in scenic Gainesville. Now of course, it takes time to erect buildings, so as just mentioned, the first academic year 1905--1906 of our current institution was actually spent on the Lake City campus while Buckman and Thomas Halls were being constructed. In Chapter 2, Appendix C, we include Proctor's [1] amusing account of the less than ebullient feelings of our faculty forebearers when they toured the construction site in March of 1906. Then in Chapter 4, we will present the move to Gainesville as President Andrew Sledd viewed it, based on Sledd's correspondence during the summer of 1906.

If we take a slightly closer look at the first faculty of the University of Florida, what we find is that with the exception of Professor James Anderson who had been in Tallahassee from 1903--1905, all of the other personnel had either been in Lake City since 1900 or so, or else had been brought in from the outside by Dr. Andrew Sledd during his building campaign of 1904--1905 during what turned out to be the last academic year of the Lake City Agricultural Institute. Thus, Proctor is able to write that from the technical viewpoint, Dean Robert Benton of Engineering was the first person to be appointed by the Board of Control, once the Buckman Act had established the University of Florida; but in fact virtually all of the other faculty simply moved with President Andrew Sledd from Lake City to Gainesville in 1906 and had already been hired during the summer of 1904.

In 1930, under the Tigert Presidency, our campus celebrated the twenty-fifth anniversary of its establishment under the Buckman Act of 1905. However, Tigert and a number of the faculty were concerned about the extremely youthful look of a founding date of 1905, when compared with various other institutions in the United States, cf. [2, p. 36]. Thus, shortly after the festivities for the twenty-fifth anniversary had ended, Tigert urged the Board of Control to change the date on the University Seal from 1905 to 1853, reflecting the date on which the State began public support of the East Florida Seminary (which commenced operations in January 5, 1852 as a private institution, cf. [2, p. 18]).

If we adopt this broader viewpoint, then, since virtually all of our faculty, including our first Professor of Mathematics, Dr. Karl Schmidt were already hired or re-appointed by Dr. Andrew Sledd during the summer of 1904 just prior to his first academic year as President of the Lake City Institution, then we should perhaps start with the Sledd Building Program of 1904. Once we do that, however, we find that the President of the Lake City Agricultural Institute from 1901--1904, amazingly enough, received the Ph.D. in Mathematics from Johns Hopkins in 1896. Thus Chapter 1 begins our story with Dr. Thomas Taliaferro in Lake City in 1901. To try and help fix the tremendous growth in scale of the University of Florida from its earliest beginnings in Gainesville at the very outset of this study, we reproduce an interesting table from [2, p. 237] which shows the enrollments at the beginning of the terms of each of the presidents of the University of Florida during the time period covered in this book:

Enrollments at the start of UF President's terms in office:
1906 Sledd 108
1909 Murphree 186
1928 Tigert 2,270
1947 Miller 8,778
1955 Reitz 10,868
1967 O'Connell 19,004
1974 Marston 28,332
1985 Criser 36,120

We conclude this introduction by commenting on several trends in American higher education which will be manifested in our early institution. First, we will see in Chapter 3 that during the first academic year in Gainesville, of the academic staff of 14 professors, over one-quarter of them, namely, Professors Anderson, Benton, Crow, Flint, and Schmidt, had received some of their advanced training in Germany. In Marsden's book on the development of the modern American university, we find the following written about study in Germany, [3, p. 104]. Here Marsden is writing specifically about Henry Tappan, 1805--1881, the first president of the University of Michigan.

"Between 1815 and 1914 about nine to ten thousand Americans studied in
 Germany.  In Tappan's day the trend had barely begun; yet Tappan's generation
established an immensely important precedent.  Throughout the rest of the
nineteenth century German universities would serve as America's graduate
schools.  It would be rare to find either a university leader or a
major scholar who had not spent some years studying in Germany.

...neither German ideals nor educational models were imported
without major adjustments to the American setting.  Germany
nevertheless had overwhelming symbolic importance.  Americans stood in
awe of the German universities. Eighteenth-century German universities
had taken the lead on the European continent and, especially after the
 establishment of the University of Berlin by Prussia in 1810, had moved
 to world pre-eminence.  For Americans, who in University building were
 behind just about every European country, an appeal to a German precedent
 could be an intimidating argument."

As a further illustration, the following is written about one of Tappan's proteges, Andrew Dickinson White, who would be the first president of Cornell University, [3, p. 114]. Also, this paragraph sheds some light on the master's degree in the mid-nineteenth century.

"As a gentlemen with no clear plans on graduation [ed., from
Yale] in 1853, White settled on accompanying his Yale friend 
Daniel Colt Gilman as an unpaid attache to the American
 diplomatic mission in Russia.  While abroad, White enrolled for lectures
  in history, art, and literature at the University of Berlin, thus sampling
 the renowned German universities, an enterprise that was becoming almost
 mandatory for aspiring American scholars.  The experience
was sufficient for him to decide on a scholarly career.

Apparently hoping to improve his chances for employment at Yale, White
returned to New Haven to receive a master of arts degree, which was still a
perfunctory degree granted after three years to virtually any graduate who
paid a fee ...."

An equally illustrious example of a Yale scientist who studied in Europe during these times is provided by J. Williard Gibbs of Yale, cf. [4]. Gibbs grew up in New Haven, attending the Hopkins Grammar School, established in 1660 as only the fourth institution to offer instruction in Latin and Greek in this country, after the Boston Latin School (1635), Harvard College (1636), and the Roxbury Latin School (1645). The entrance requirements for Yale in 1854 included Latin, Greek, English grammar, geography, and in mathematics, Thomson's Higher Arithmetic and Day's Algebra. After taking his undergraduate degree at Yale, Gibbs entered what was then called the Department of Philosophy and Arts at Yale in the fall of 1858 as a graduate student in engineering; as a senior Gibbs won two scholarships in student competitions, one of which carried the obligation of continuing with graduate work at Yale. In June, 1863, Gibbs received his Ph.D at Yale, as one of three doctorates. This was only the third year that Yale had awarded this degree and Gibb's thesis was apparently the second in science and the first in engineering to be awarded in this country, according to [4, p. 32]. Following upon receipt of the doctorate, Gibbs received an appointment as a tutor at Yale for the usual three year period. It is amusing to read that teaching assignments were made according to seniority, so that even though Gibbs' strong suit was science and mathematics, he found himself receiving the assignment as the Latin tutor, while another more senior gentleman who later would head the Latin Department at Yale was serving as the mathematics tutor. After this time period, Gibbs left in August, 1866 for a three year period of study in Europe. The first academic year 1866--1867 was spent in Paris. Gibbs' notebooks reveal that he attended the lectures of Chasles on higher geometry, Duhamel on higher algebra, Liouville on number theory and on rational mechanics, Serret on celestial mechanics and elliptic functions, Darboux on mathematical physics, specifically, on the mathematical theory of heat, and finally Bertin on experimental physics. Delauney was offering material on applied physics, but Gibbs did not attend his lectures. Also, Gibbs spent a good deal of time reading articles and books of Lagrange, Laplace, Poisson, Fresnel and Cauchy. So here Gibbs set himself a schedule calling for sixteen hours of lecture attendance per week, as well as independent reading. It is not surprising, especially as his constitution was not the strongest, that he became ill from overwork and had to recuperate on the Rivera, fearful of having contracted tuberculosis. The next academic year 1867--1868, Gibbs spent in Berlin. There, having learnt from experience, Gibbs did not try to pursue such an ambitious program of studies. One of the still surviving aspects of the German academic system, is that each university student keeps a Studienbuch recording on a yearly basis his/her program of lecture courses, exercise sections, and seminar participations. The Yale Archives retains possession of Gibbs' Studienbuch, so that we learn that in Berlin Gibbs signed up during the first semester to follow the lectures of Magnus on general physics, Kundt on acoustics, Weierstrass on determinants, Kronecker on quadratic forms; and during the second semester, the lectures of Magus on technology, Quincke on acoustics and capillarity, Foerster on least squares, Weierstrass on analysis, and Kummer on probability calculations. The next year Gibbs spent in Heidelberg, but no surviving documentation exists according to [4] which would indicate what Gibbs studied during his final academic year in Europe.

Second, Professors Anderson, Farr, and Taliaferro of the early days of our institution, who had not received their Ph.D.'s in Germany, had received their doctorates at Johns Hopkins. This university originated from the bequest of a wealthy Quaker businessman, Johns Hopkins, who provided funding in 1874 in his will for the founding of a university in Baltimore. Marsden writes the following about Johns Hopkins in [3, p. 150].

``The Johns Hopkins University opened its doors in 1876 and remained under 
[Daniel Coit] Gilman's leadership until his retirement in 1901.  Unlike his
situation in California [at Berkeley], Gilman had almost complete control over
his institution.  One of the legacies of the old-time colleges that
the founders of the new universities typically retained was the wide
discretionary power of the president.  With a relatively free hand to
 implement his dream for a university, Gilman quickly built Johns Hopkins
 into America's leading graduate university, setting the standards for others to

Professors John Thompson and Peter Sin of our own department have both commented to me that it is remarkable that a course in Galois theory was offered at the University of Florida from its inception in 1906. No readily accessible text treating this topic in algebra was available until much later. It may also be noted that at the inception, a course entitled the mathematical seminary was offered. Marsden has the following comments on the introduction of the graduate student---faculty seminars into the American University, starting at Johns Hopkins, cf. [3, p. 153]

"German Lehrfreiheit---the freedom for the guild of professors
independently to pursue its inquiries, publications and teachings---became
 a symbol for an emerging idea of academic freedom.  This idea,
in the minds of American reformers such as Gilman, was inextricably
mixed with the simple ideal of pure scientific investigation, or the
pursuit of truth.  The graduate seminar was an important forum in which such 
investigation could take place.  The seminar had developed in Germany
as a model of how the research ideal and the humanistic ideals could
be combined. It simultaneously stressed individual attention from
professors, original scientific research, individual creativity, and
honing of critical skills."

The inspiring effect this transplanted institution had on graduate students in the early 1900's is most vividly revealed in recollections about the Seminar held at Clark University in a special room in President G. Stanley Hall's home, cf. [5, p. 53]. Hall had engaged in studies in Germany prior to obtaining the first American Ph.D. in Psychology from the philosophy department at Harvard in 1878.

``Hall's most effective teaching was done in his famous Monday evening
 seminar. About 7:15 P. M. each Monday, all students in philosophy,
 psychology and education, and perhaps also faculty and invited guests,
 would gather in Hall's home across the street from the campus.  Typically,
two students each session would report on their own investigations or
summarize the literature of a given field in a written paper.  After
the first, Hall would lead off the discussion and call for reactions. 
 After thirty to sixty minutes of fiery debate, in which he might join,
Hall would summarize the principal points and all would adjourn to the
 dining room for light refreshments.  About 9:30 the second presentation
 would begin, and the meetings rarely broke up before midnight.  Early on,
the seminar was focused on specific readings, and sometimes an invited
lecturer would make a presentation. But in its mature form the Monday
evening seminar was the students' time on the frontiers, and as one of
them, Lewis Terman, recalled the sessions,

`I always went home dazed and intoxicated, took a hot bath to quiet my
nerves, then lay awake for hours rehearsing the drama and formulating
all the clever things I should have said and did not.' 

 Hall himself in retirement, missed the seminar experience
more than anything else, and felt a peculiar lonesomeness each
Monday evening.''

A third aspect of the pre-history of the Gainesville campus and such a practical thing, from some viewpoints, as the teaching mission of a department of mathematics at a large state university, is that our precursor, the Lake City Agricultural College was established based to some degree on funding provided by the Hatch Act and also the second Morrill Act of 1890, cf. [2, p. 21]. Here is what is written about the philosophical underpinnings of the first Morrill Land Grant Act of 1862 in [3, p. 115].

``... This act [Morrill Land Grant Act of 1862] represented the
culmination of popular agitation for higher education in the
mechanical and agricultural arts, a proposal that promised to help
make the United States competitive in economic and industrial development.
The cause was part of the emerging Republican agenda
to develop the nation industrially and morally.

 `We want a seminary,' inveterate reformer Horace Greeley declared in 1858, 
which provides as fitly and thoroughly for the education of the Captains of 
Industry as Yale or Harvard does for those who are dedicated to either of
 the Professions.'

In 1858 the act had been passed by Congress but vetoed by President
 Buchanan as an unconstitutional infringement of the federal government.
  With the southern states absent in 1862, the way was cleared for the
 passage of the act, which was signed by Lincoln on July 2, 1862. The
 act provided for the proceeds from large tracts of public land to go
 to the establishment and support of colleges of agricultural and mechanic


  1. Proctor, Samuel, The University of Florida: Its Early Years, 1853--1906, Dissertation, University of Florida, February, 1958.
  2. Proctor, Samuel and Langley, Wright, Gator History, A Pictorial History of the University of Florida, South Star Publishing Co., Gainesville, Fl., 1986.
  3. Marsden, George, The Soul of the American University, Oxford University Press, New York, 1994.
  4. Wheeler, Lynde, Josiah Williard Gibbs; the History of a Great Mind, Yale University Press, 1952.
  5. Koelsch, William, Clark University 1887--1987, Clark University Press, Worcester, Massachusetts, 1987.


I am first of all indebted to Norma Sue Ehrlich, my poor, long suffering wife, who has had to endure several years of listening to me ramble on about the early pioneer builders of the University of Florida as the manuscript has grown longer and longer. It has been very gratifying to have been able to study first hand from archival sources at the University of Florida Archives in Smathers Library the early struggle to get our current institution established, prior to World War I. The Archives Staff, especially Carl Van Ness, are to be complimented for their helpful assistance in this task. I have fond memories of my first timorous steps into Library East, at which time Carl first steered me toward the old university catalogues and records, and pointed out to me Dr. Herbert Keppel, as an early Professor of Mathematics and Astronomy. Several months later, Carl recalled materials left by Herbert Keppel that were stored in the Ben Hill Griffin Stadium at Florida Field, and Vann Ness's retrieval of these materials was directly responsible for the existence of the chapter on ``Graduate education in 1894.''

It has been a real pleasure to learn first hand from Mrs. Lillian Pirenian about President Murphree, Dr. Thomas Simpson, and Professor Zareh Pirenian; to correspond with Reverend Leonard Blanton about Dr. Thomas Simpson; and to correspond with Dr. John Benton about his father Dean John Benton, the founding Dean of the Engineering College. We had an informative telephone conversation with Dean John Maxfield of Louisiana Tech, who was Chairman of Mathematics in Gainesville from 1960--1967, which gave us his own personal perspective on airconditioning Walker Hall and recruiting A. D. Wallace. This was followed later by an hour long interview of Dean Maxfield, which he kindly granted me while we were both attending a winter meeting of the American Mathematical Society in Orlando during January, 1996. We were further fortunate to receive correspondence from Professor Wayman Strother during May, 1996, giving us his perspective of the A. D. Wallace appointment from the viewpoint of a second senior faculty member who was intimately involved in the recruitment process during the early 1960's. In addition, we have benefitted from a visit to the home of Professor S. Gould and Doris Sadler, correspondence with Mrs. Robert Blake and with Professor Robert Meacham (of Eckerd College), lots of recollections from Mrs. Edwin Hadlock relayed to me by her daughter Nancy, and lots of recollections from Professor Theral Moore, who joined the department in 1955, and his wife Nancy Moore. Professors Louis Block (who personally experienced University College), Al Bednarek, Kermit Sigmon, Jed Keesling, Beverly Brechner, Zoran Pop-Stojanovic, Jorge Martinez, Charles Nelson, Steve Saxon, and Rhoni Khuri have kindly responded with their recollection of events occuring in the 1960's and 1970's. Professors Gerard Emch, Antoinette Emch-Derriaz, Joseph Glover, Ralph Selfridge, Rick Smith, Alexandre Turull, and Chris Stark have helped me with a number of insightful comments, and Stark especially provided me with archival material from the University of Maryland pertaining to President Taliaferro of the Florida Agricultural College in his later more successful tenure at the University of Maryland. Professor Bob Burton Brown, who was the last Dean of University College, has kindly provided me with information about that institution. Reverend and Mrs. Benson Cain have also been helpful in recalling Mrs. Cain's girlhood days in Gainesville; Mrs. Cain's father graduated in the class of 1916 and she knew Dr. Thomas Simpson from attending the First Presbyterian Church. I also have benefitted from conversations with Professor Thomas Fay, Professor Hugh Cunningham, Lucius B. Gravely III (another U. F. alumnus who had Professor Franklin Kokomoor as a Sunday school teacher while attending our University during the early 1940's), Henry L. Gray Jr., Daniel Harmeling, Mrs. Winston Little, and Professor Phillip Bradshaw. It is also a pleasure to thank Mrs. Richard Ehrlich for calling my attention to George Marsden's book, The Soul of the American University, and for providing me with information about the University of Illinois prior to and during World War II. Dr. Richard Ehrlich has kindly provided me with helpful comments concerning the role of mathematics in industry prior to and after World War II. We also thank Sarah Hong and the Carleton College Archives, Northfield, Minnesota for providing us with materials about our very first Head Professor of Mathematics and Astronomy, the German native Dr. Karl Schmidt.

I systematically wrote to the Ph.D. alumni from the 1950's, and am grateful for information provided to me about their careers and student days by Drs. John Neff, Mary Neff, John Kenelly, Jane Day, Jan Andrus, Richard Yates, Thomas Horton, William Hare, Alvin Owens, and Emmet Low. University of Florida historians Dean Michael Gannon, Professor Fredrick Gregory, President John Lombardi, and Professor Samuel Proctor (and his staff at the Florida Oral History Project) are also to be thanked for their kind encouragement of this project. Especially, as a result of Professor Proctor's extensive research in the Florida Oral History Project, we were able to posthumously learn from our former chairman Professor Franklin Kokomoor about his views of the development of the University from 1928--1960, posthumously learn from Mrs. Elizabeth Simpson about our third chairman Dr. Thomas Marshall Simpson, who served as chair from 1918--1951 and Dean of the Graduate School from 1939--1951, and posthumously learn from Mrs. John Benton about life in Gainesville in the 1910's and about Dean Benton and his efforts to build the Engineering School from 1905 up until his untimely death in 1930. (Mrs. Emily Ring is also deserving of our thanks for having taken the time to interview a number of these early figures in this Oral History Project). Professor Edward Keuchel and Dr. Robin Sellers of the Department of History of Florida State have helpfully supplied me with certain facts relating to President Albert Murphree and information they obtained from the Florida State Archives.

The current chair of the Mathematics Department, Professor Joseph Glover, was in on the inception of this lengthy project; when he told me that he had lists of all of the masters and Ph.D. graduates, I embarked on a project of writing to the alumni of the 1950's, hoping to gain some material for the Walker Hall Review. I never at all envisioned that I would wind up in the Archives reading presidential correspondence from 1904 and 1906!! Dean Gannon kindly informed me that I could find a complete set of catalogues in the Archives, and then later Professor Proctor suggested that I look in the Sledd Letterbooks, whatever they were, to try to find correspondence from Sledd to his early appointees. So that is how the library work all got started. Professor Glover has also provided me with some insightful comments in many discussions we have held on how the mathematics community moved into what we arrogantly would call ``modern times,'' as well as encouraging me in my pursuit of this lengthy and unconventional endeavor.

Professor Paul Ewing Ehrlich
December 3, 1996