Recently, an extensive investigation of the emergence of the American mathematical research community has been given in Parshall and Rowe [1]. The authors argue in this volume that while certainly there were instances of research activity in the United States during the 1700's and 1800's, like the Lawrence Scientific School and Benjamin Peirce at Harvard or the Sheffield Scientific School and Hubert Ansom Newton at Yale, that critical mass in terms of creating a sustainable research community was not achieved until the late 1800's. In this general time period, to give three prominent examples, the amassment of certain industrial fortunes enabled benefactors Johns Hopkins to establish Johns Hopkins University, primarily for graduate education; Jonas Clark to establish Clark University; and John D. Rockefellar to establish the University of Chicago as a Baptist institution of higher learning. In [1], three phases in the emergence of our research community are detailed:
In [2], we have investigated in detail how this pattern may be found in the University of Florida faculty at the turn of the century. In particular, during 1905 1906 when the current institution came into being as a result of the Buckman Act of 1905, we found one individual, Dr. Karl Schmidt, as the sole faculty member in the Department of Mathematics and Astronomy. Also, we were able to determine that Schmidt, who had received the Ph.D. from Marburg in 1898, was a German native who had married a Boston lady he had met while he was studying in Berlin and she was visiting Berlin, rather than an American who had studied abroad.
Since we had done extensive work on the development of the University of Florida during 1904  1906 in [2], it seemed appropriate for comparison purposes to look at the University of Missouri Department of Mathematics in this same time frame. This would also be toward the end of Richard H. Jesse's presidency at Missouri, which lasted from 1891 until 1908, when Jesse retired in his mid fifties, his health apparently ruined from overwork. Jesse was a son of the South, who had not taken any kind of doctoral work abroad, or indeed, any doctoral work whatsoever. He was born in Virginia in 1853 and educated at Hanover Academy and the University of Virginia. In the midst of his studies at Virginia, in a not uncommon career pattern for some during that time period, he returned to Hanover Academy to teach French and mathematics, before undertaking further work at the University of Virginia. In 1878, the University of Louisiana reopened after the Civil War, and Jesse, still a student at Virginia, was unanimously recommended by the Virginia faculty as the Dean of the Academic Department, and Professor of Greek, Latin, and English at Louisiana. Shortly thereafter in 1882, when Tulane University was first organized, Jesse was appointed as the first Professor of Latin. Then in 1891, not yet forty years old, Jesse came to Columbia to take on the presidency of the University of Missouri. Stevens [3, p. 355] has written:
"President Jesse's discrimination in the recruiting of new members of the faculty so as to secure men of intellectual competency as well as teaching and administrative ability became so well known that in future years people looked back upon his presidency as the Golden Age of the University."
Having no other means of judging the veracity of Dean Stephens' statement, we will let the reader judge for herself or himself based on the evidence provided by the Catalogues of the University of Missouri during that time period.
In contrast to the one man Department of Mathematics and Astronomy at the frontier University of Florida in 190506, the Missouri Record reveals the following: first, in the April 16, 1906 Report of the Board of Curators to the Governor and State Legislature we find the following written [4]:
"In the summer of 1905, Dr. G. A. Bliss, Assistant Professor of Mathematics, resigned to accept a position at Princeton. Dr. Oliver D. Kellogg, has been elected as his successor. Mr. Louis Ingold, Instructor of Mathematics, has been granted a leave of absence. This, together with the large enrollment in Mathematics, has made it necessary to appoint two additional instructors in that subject. Dr. (sic) R. L. Borger and Dr. W. D. A. Westfall have been appointed. During the summer, Miss Emily E. Dobbins resigned her position as Assistant in Mathematics. To fill the vacancy thus created, Mr. E. S. Haynes has been appointed Assistant for this session."
The first sentence is in itself a testament to the Jesse recruitment standards, for Bliss would go on to become a leading figure in the calculus of variations in America, producing many Ph.D. students at the University of Chicago.
Second, here is how the Missouri Department of Mathematics faculty listing appears in the 190506 Catalogue:
"Mathematics Professor HEDRICK; Professor DEFOE; Assistant Professor KELLOGG; Dr. AMES; Dr. WESTFALL; Mr. INGOLD; Mr. BORGER: Miss WALKER; Mr. HAYNES."
When I first saw this list, in a copy kindly sent to me by Professor John Beem as I prepared for my lecture in the Conference on Continued Fractions: From Analytic Number Theory to Constructive Approximations honoring Professor L. Jerome Lange's retirement, my heart almost skipped a beat. For in my possession is the first yearbook (in 1900) from one of the predecessor institutions to the current University of Florida, called variously the Lake City Agricultural Institute, the Florida Agricultural College, or the University of Florida during the different years of its existence. The Professor of Mathematics at the Lake City Agricultural Institute during the academic year 1899 1900 was one R.L. Borger, who would find himself dismissed during the summer of 1904 when the new outside President Andrew Sledd wished to appoint a man with the doctorate and postdoctoral experience at Harvard, Dr. Karl Schmidt, whom I mentioned above. Could these two Borger's be the same person, what an amazing coincidence that would be!
Here is an example of how helpful those turn of the century catalogues are; the listing for Borger is as follows, just to reproduce one of these entries in its entirety, cf. [4]:
"Robert Lacy Borger, A.B., A. M.; Instructor in Mathematics A.B., University of Florida, 1893; Instructor in Mathematics, Southern Collegiate Institute, Albion, Illinois, 189394; Graduate Student, Johns Hopkins University, 18945; Assistant Professor of Mathematics, University of Florida, 189698; Professor of Mathematics, 1898 1904; Graduate Student, University of Chicago, Summer Quarters, 1898,'99,1900,'01,'02 and the year 190405; A. M., 1905, Instructor of Mathematics, University of Missouri, 1905  ."
How fortuitous  the Ole Mizzou catalogues reveal what was previously unknown : (i) Borger fits the hardscrabble pattern (recall Jesse) of working one's way up through the ranks, without the privilege of doctoral study after obtaining the B.A., but continuing graduate work piecemeal during summers, and with an occasional full year of study; (ii) Borger's early work was taken at Johns Hopkins University; (iii) Borger's case also illustrates how Chicago as part of its service mission during the early 1900's provided graduate education during the summer session to raise the level of those individuals in our national mathematics faculty, who were teaching without yet having attained a doctorate.
How do the other Missouri faculty fit the pattern (I)  (III) given above? Note first as is typical outside of a few lucky departments in those times, that there is only one full time position with rank of Professor, and naturally, that person would be expected also to serve as Chair, even if that title did not exist then in many of our institutions. (The exceptional case of Profesor Defoe will be explained below.) In the "life isn't fair" category, we find that two friends from doctoral work in Goettingen under Hilbert, Professor Earle Raymond Hedrick, and Assistant Professor Oliver Dimon Kellogg, are together at Missouri, albeit with highly different ranks. Hedrick had obtained his dissertation in 1901 with the topic "Uber den analytischen Character des Losungen von Differentialgleichungen" and Kellogg in 1902 with the topic "Zur Theorie der Integralgleichungen und des Dirichlet'schen Prinzips." Hedrick would serve at Missouri from 1903 until his relocation to UCLA in 1924; Kellog would serve at Missouri from 1905 until his relocation to Harvard in 1919.
The University of Missouri Catalogue [4] helps fill in a few details on Hedrick's life not spelled out in Parshall and Rowe [1]. Hedrick (1876  1943) took the A.B. from Michigan in 1896, then studied at Harvard, especially with Maxim Bocher and William F. Osgood. He then received a Parker Fellowship to Goettingen, and thus was able to take the doctorate under Hilbert in 1901 as previously noted. In [1], the authors write that Hedrick then studied in Paris where he met Goursat, Picard, Hadamard and Appell. In [4], it is recorded that Hedrick was a student at the Ecole Normale Superieure during the second semester of 1901. Hedrick spent 1901 1903 as an Instructor at the Sheffield Scientific School at Yale before coming to Missouri in 1903 as Professor of Mathematics. In addition to his research, Hedrick played an important role in building up the American mathematical infrastructure, cf. [1]. He was an editor of two series of textbooks: one of mathematical subjects for secondary schools and colleges, and a second series in engineering mathematics, "A Series of Mathematical Texts and Engineering Science Series." He was involved in translating both Felix Klein's Elementary Mathematics from an Advanced Standpoint into English from German, and Edouard Goursat's A Course in Mathematical Analysis from the French into English. In this later endeavor, he thanks W. F. Osgood of Harvard, with whom Hedrick had studied as a graduate student, for suggesting the undertaking of this project. Hedrick was involved in the activities of both the American Mathematical Society and the Mathematical Association of America. Just to give a few examples, he served as an editor of the Bulletin during 1921  1937 and served as first President of the Mathematical Association of America. He is of course commemorated by the Hedrick Lecture Series of that second association.
Oliver Dimon Kellogg took the A.B. degree at Princeton in 1899 and the A. M. in 1900. He held the J. S. K. Fellowship at Princeton during 1899 1902, which enabled him to study abroad at Goettingen, and take the doctorate under Hilbert in 1902 as we mentioned above. During 1903  1905, Kellogg was an Instructor at Princeton before coming to Missouri in 1905 as Assistant Professor of Mathematics, filling the position created by Bliss's removal to Princeton as we noted above in the Board of Curators report.
In the basement of the University of Florida Science Library, I located the following testimony to the presence of Hedrick and Kellogg at Ole Mizzou,[6]:
APPLICATIONS OF THE CALCULUS TO MECHANICS BY E. R. HEDRICK Professor of Mathematics in the University of Missouri and O. D. KELLOGG Assistant Professor of Mathematics in the University of Missouri
GINN AND COMPANY Boston . New York . Chicago . London COPYRIGHT, 1909, BY E. R. HEDRICK AND O. D. KELLOG
Current faculty at Missouri may enjoy the following quotation from the preface revealing educational issues of the early 1900's:
"Wherever the teaching of mathematics to engineering students is discussed, and frequently in cases of other classes of students, the criticism which is almost without exception the most insistent is this: that the student leaves the course without adequate ability to apply his mathematical knowledge. This means that he has not the faculty of taking a problem, giving it an analytic formulation, and interpreting the analytic results. It is an open question whether it is the duty of the teacher of mathematics, or of the teacher of the more technical work which involves mathematics, to supply the needed training, but usually the mathematician is glad at least to share the responsibility and to do whatever he can to make his work fruitful, fully conscious of the fact that if he can successfully make the contact of his subject with the problems of the laboratory, of the engineering office, and of other activities, he will thereby add immensely to the vitality and interest of his work. With such a motive, it has been the practice at the University of Missouri to follow the course in sophomore calculus with several weeks in applications to mechanics, this being a subject rich in the kind of material desired. The present book is a formulation of the work there attempted, and it is believed that the need of our institution which has called the book into being will make its appearance welcome to a large number of mathematical departments."
During my days as an Assistant Professor at Missouri, I recall it being mentioned in the lounge that Hedrick had been at Missouri a long time, and this has been borne out by the evidence above, that Bliss had been at Missouri, and also the name Westfall was mentioned. Indeed, Professor John Been reminded me of a story about Westfall's standard grading practices in the calculus of variations course which is a good illustration of the power held by faculty in the prestudent teacher evaluation days; it is alleged that Professor Westfall always assigned grades of A to the mathematics graduate students, grades of B to the mathematics undergraduates, and grades of C to the engineering students taking this course. Prior to consulting the Missouri catalogues, I had no other information on Westfall apart from a few sentences like the unadorned comment on [3, p. 359] that Kellogg and Westfall were both prominent in the later history of the University of Missouri. But the catalogues revealed that Wilhelmus David Allen Westfall, Instructor of Mathematics, during 1905 06, would have been a student at Yale when Hedrick was an Instructor at Yale. Westfall took the A.B. at Yale in 1901, then held the Douglas Fellowship at Yale during 1901 02 and then held the position of Acting Instructor in Mathematics at Yale College during 1902  03 (that was the undergraduate division). Westfall studied in Goettingen during 1903  05, receiving the Ph.D. in 1905, and then came to Missouri for the 1905 06 academic year.
What do the catalogues reveal about the other instructor, Dr. Lewis Darwin Ames? He taught as an Instructor of Mathematics at Chillicoth Normal School during 1890  1900, while studying at Chicago during the summers of 1897 and 1898. He received the degree of B. L. from the University of Missouri in 1899, then went on to Harvard, receiving the A.B. in 1901, the M.A. in 1902, and the Ph.D. in 1904. He served as an Instructor in Mathematics at Harvard during 1901  1902, had the good fortune to be a Graduate Scholar in Mathematics during 19021903, then came back to Missouri as an Instructor in 1903, while finishing work on his dissertation.
The catalogue also revealed four people on the faculty teaching without the Ph.D., Mr. Ingold, Mr. Borger, Miss Walker, and Mr. Haynes. We have already discussed Robert Borger above. Louis Ingold, A.B., A.M., Instructor of Mathematics, was a Student Assistant in Mathematics at the University of Missouri during 190001, taking the A.B. in 1901. Then he served as a Teaching Fellow in Mathematics during 190102, taking the A.M. in 1902. He was a graduate student at the University of Chicago during 1902 and also on leave there during 190506. He held the title of Acting Assistant Professor of Mathematics at Missouri during 190203, then Assistant in Mathematics during 190305, then Instructor of Mathematics during 190506 while he was on leave at Chicago. Mary Shore Walker is teaching with the title of Assistant in Mathematics; she received the A.B. from Missouri in 1903 and the A.M. in 1904, so this provides an example of a promising homegrown young person teaching for Mizzou after receipt of the masters. Eli Stuart Haynes, Assistant in Mathematics, is on the staff, after receipt of the A.B. in 1905. (Haynes would later serve as Chair of Astronomy at Missouri for many years as well as being the husband of long time mathematics faculty member Dr. Nola Haynes, who was profiled in the Summer 1997 issue of the Missouri departmental newsletter.)
Especially with the upgrade of the Luther Marion Defoe Distinguished Professorship during the Lange chairmanship, many have wished to know more about this somewhat mysterious figure from the past, who is listed as Professor Defoe in the 190506 Departmental listing, with sole teaching responsibility, the graduate course Mathematics
20. Analytical Mechanics. Open to any who have taken courses 7a and 7b. Three times a week. Hours to be arranged. (Alternate years. Given 1905  06.) Professor DEFOE.
Fortunately, the old catalogue itself reveals more about Professor Defoe; he is one of the home grown products who WAS in fact responsible for the instruction in mathematics prior to the Jesse upgrade in staff quality discussed above. Defoe has quite a title in the 1905  06 catalogue; he is "Professor of Mechanics of Engineering, Professor of Mathematics in the Teachers College, and Tutor to the University" all this with only the A.B. degree.
The catalogue reveals that Defoe was Fellow in Mathematics at Missouri during 189192, then took the A.B. at Harvard during 1893. Then he returned to Missouri where he taught mathematics under various titles; including Acting Professor of Mathematics during 189798. But then during 18981902, his title was downgraded to Assistant Professor of Mathematics, (when John Fellows was Chair according to Professor Casazza's note in the Summer 1997 Critical Points issue). During 19021903, Defoe studied abroad, but in Cambridge, England, rather than in Germany. He returned to Missouri and held the title of Tutor to the University since 1904, Professor of Mechanics since 1902, and Professor of Mathematics in the Teachers College since 1904.
What is Defoe teaching in these other departments? Let us start with the Teachers College. We find the following entry for the 1903  1904 academic year:
Teachers College Mathematics Professor Defoe
1. Trigonometry and Analytic Geometry M.W.F., at 11:30
2.Advanced Algebra T.Th.S., at 10:30
3a. The Teaching of Mathematics. Lectures and discussions on the teaching of mathematics with special references to high school instruction. Two hours. Hours to be arranged.
What about this "Mechanics"?? We find the following entry under the College of Engineering.
Mechanics Professor Defoe
3. Mechanics of Engineering. Statics, dynamics, strength of materials, hydrostatics and hydrodynamics. Lectures, W.F., at 8; Recitations, Section I, T.Th.S., at 8; Section II, T.Th.S., at 9.
4. Elasticity. Mechanical theory of elasticity. T.Th.S., at 10:30.
9. Hydromechanics. An elementary course in hydrostatics and hydrodynamics. M.W.F., at 10:30.
12. Fourier Series and Potential Functions. Recitations and lectures. Hours to be arranged.
20. Problems in Mechanics. Dynamics of a rigid body. M.W.F., at 11:30.
27. The Theory of Sound, with special reference to the Partial Differential Equations of Mathematical Physics. Reading course, based on Rayleigh's Theory of Sound. Three hours. Hours to be arranged.
Unfortunately, I did not track down what it meant to be "Tutor to the University."
That is certainly a daunting array of potential courses for Defoe! What did the other faculty teach? As is true today, there are a variety of algebra offerings, then charmingly called Short Freshmen Mathematics (three times a week) and Extended Freshmen Mathematics (5 times per week). While the Short Freshmen Mathematics covered Trigonometry andAlgebra the first semester and Plane Analytic Geoemtry the second, the Extended Freshmen Mathematics also included Solid Analytic Geometry as well as a deeper treatment of algebra. Two varieties of calculus were offered:
3. Short Course in Calculus. Three times a week. A cultural course for those who can take only three hours. It contains the essentials of the Calculus, a few applications, supplementary work in Analytic Geometry. Many difficult theorems and problems are purposely omitted. Students intending to make Mathematics a speciality should take 4(E) instead of 3; unless they elect 6 at the same time; but 3 is a sufficient basis for recommendation for high school teachers. T.Th.S., at 8. Dr. AMES.
4(E). Extended Course in Calculus. Five times a week. A more detailed and extensive course in Calculus proper than course 3, followed by special supplementary courses in Differential Equations and in Mechanics. Students inclined toward Mathematics should elect this course, or the combination of the courses 3 and 6. In it they can decide whether or not they can succeed in further work in Mathematics. Five sections; three sections daily (except S.) at 8, 9, and 11:30, respectively; two sections daily (except M.) at 8 and 11:30 respectively. Texts, rooms, and instructors posted in advance.
What more advanced courses are the faculty teaching (in alternate years)? Professor Hedrick, Professor of Mathematics, offered the following courses:
5. Second Course in Calculus using Goursat's Course in Mathematical Analysis
9a. or 9b. Mathematical Laboratory (non credit) the construction of mathematical models, something popular with Felix Klein, cf. [1].
14. Theory of Functions of a Real Variable
15. Function Theory, Complex Variables, Elliptic Function Theory
23. Theory of Functions
We have already noted that Professor Defoe offered the graduate course 20. Analytical Mechanics but had primary teaching responsibilities elsewhere by 1905  06.
Assistant Professor Kellogg was responsible for the following courses:
6a. Theory of Equations and Determinants
13a. Fourier's Series and Allied Series
13b. Potential Functions. This course presupposes the preceding (13a). It forms an introduction to Mathematical Physics. Lectures, supplemented by reading. Three times a week. Hours to be arranged. (Alternate years). Assistant Professor KELLOGG.
18a. or b. Partial Differential Equations of Mathematical Physics
19. Theory of Numbers; First Semester : Classical Theory; Second Semester : Algebraic Numbers
27. Mathematical Theory of Sound (or Heat).
Dr. Westfall, Instructor in Mathematics, was a specialist in differential equations, as has been recalled to me when I was on the faculty at Missouri. He was responsible for
7a. Elements of Differential Equations; text: Murray's Differential Equations
8b. Elements of Projective Geometry; possible texts: Emch, Projective Geometry Reye, Geometrie der Lage Scott, Modern Geometry
16. Theory of Differential Equations; First semester: ODE's; Second semester: PDE's
21a. or b. Integral Equations
In the teaching of Dr. Ames, Instructor in Mathematics, we find confirmation of what had been rumored to me when I was a new Assistant Professor at Missouri; that the department had a long tradition of offering differential geometry. Note also, recalling Sophus Lie's role in inspiring the wanderlust generation (II) of American students abroad, that a course in Lie's theory was offered at Missouri in the early 1900's!! Here is the list of courses which fell within Ames' bailwick:
3. A Short Course in Calculus
6b. Advanced Analytic Geometry
8a. Elements of Differential Geometry Lectures supplemented by reading. Introduction to the theory of modern differential geometry. Reference books: Joachimstal, Niewenglowski, Bianchi, Darboux.
12a. Infinite Series and Products, using Osgood's Infinite Series and Ency. der Math. Wiss. IA3
12b. Galois' Theory of Substitutions using Dickson, Galois' Theory
17a. Theory of Groups
17b. Lie's Theory of Continuous Groups, with Applications to Differential Equations and Contact Transformations. Lectures based on Lie's works.
29b. Theory of Algebraic Invariants. Alternate with course 11b.
11a. or b. The Mathematical Theory of Probability, with Applications to Life Insurance and statistics
The reader might enjoy seeing some enrollment data as an aid to picturing how much smaller our institutions were at the turn of the 20th century than today. In 1891, at the beginning of the Jesse presidency, the Missouri enrollments, including preparatory students taking the final years of high school work, was 487. By 1901, Jesse had eliminated the preparatory division, and the enrollment in Columbia was 1,304 and at the Rolla School of Mines (which then was part of the University of Missouri in Columbia administratively) was 177. By 1908, the enrollments were 2,307 in Columbia and 229 at Rolla. In 1904, the Engineering Enrollment was 360 students. By contrast, on the Florida frontiers, the enrollments including Subfreshmen students in 1905 was 135 and in 1911 was 302. It was not until the Roaring Twenties that the Florida enrollment in Gainesville reached over 2,000 students, with an enrollment of 2,073 in 1927 for example. Faculty and townspeople of that generation regarded growing the enrollment in Gainesville to over 2,000 as a major achievement of the Murphree presidency, cf. [7].
Here are a few more miscellaneous tidbits from the early catalogues. With the smaller scale of operations as suggested above by the enrollment data, all lectures presented at the University were recorded in the catalogue. Thus we find that in 190506, exactly one outside lecturer in mathematics was featured, and it was on November 10, 1905 when Dr. T. J. J. See, Professor of Mathematics for the United States Navy Academy, spoke on "Recent Progress in Solar Research." The catalogues also reveal that Missouri offered about 20 positions of University Fellow or University Scholar spread among all the departments. In 190506, mathematics did not receive any of these awards, but in 190405, Helen Belle Montgomery, A.B. in Mathematics from the University of Missouri, was a University Scholar. Also, the 190506 Catalogue has the following charmingly titled position for the different departments and Mathematics weighs in with: Student Assistants William Abraham Hurwitz, A.B., B.S. "Problem Reader in Mathematics" .
Since I have now spent over a decade at both the University of Missouri and the University of Florida, I will indulge myself in ending this essay with another Florida/midWest coincidence that I noticed as I was preparing to speak at the Lange retirement conference. Ellery William Davis received the Ph.D. from Johns Hopkins in 1884 under the direction of Cayley, who came to Hopkins in order to visit Sylvester, the Professor of Mathematics then. During 1884  1888, Davis served as Professor of Mathematics at the Lake City Agricultural Institute. Disappointed by the level of support for higher education in frontier Florida, cf. [5], Davis left for greener pastures at the University of South Carolina. A little bit later, disappointed with the general condition of things in the entire South, Davis became Professor of Mathematics at the University of Nebraska. There Davis would coauthor a textbook, The Calculus, in a series edited by Hedrick, published in 1912. Somewhat earlier, cf. [1, p. 410], in December, 1906, Earle Hedrick, Alexander Chessin, and Ellery Davis met in Columbia, Missouri, and formed the Southwestern Section of the American Mathematical Society, with an initial membership of 35. But not until 1929, would the American Mathematical Society recognize sectional meetings (held outside of the East coast) as regular meetings of the society.
Postscript: After I sent a copy of Mizzou Mathematics in 1905  1906 to Professor Emeritus W. Roy Utz, Utz kindly wrote me a letter in response containing his personal recollections on some of the people I had described in my essay:
"I remember some of the people who you cite. For example, I knew Westfall from 1941 until his death. He was colorful and 'of the old school.'
Louis Ingold died in 1935. He was a geometer, directed several Ph.D. dissertations (including that of Nola Haynes, nee Anderson) and was an editor of the Transactions of the American Mathematical Society.
Missouri's first Ph.D. was earned by L. L. Silverman in 1910. He became known via his work in summability. He went from Missouri to Dartmouth and then, when he retired, worked for a few years at the University of Houston.
Blumenthal came to Missouri the year after Ingold's death (thus, 1936).
One of Missouri's major attractions for me was the library. You took an interest in the library, I recall, and so know that we have superb holdings in complete runs of journals and in collected works of various mathematicians (generally, these occur in Ellis Library). We need to thank Bliss, Hedrick, Kellog for this early attention to journals."
Professor Paul Ehrlich
Department of Mathematics
University of Florida
Gainesville, FL 32611
Mathematics Department

Phone (573) 8826221

© 2009 — Curators of the University of Missouri
