### The First 150 Years

*A talk by Wilfred Kaplan at the dedication of East Hall on Oct. 17, 1997*

This is an overview of the story of the Mathematics Department in Ann Arbor. I provide some "snapshots."

September 25, 1841. University first offers classes. There are seven students and two professors, Reverend George P. Williams teaching mathematics and science, Reverend Joseph Whiting teaching Greek and Latin.

1854. There are sixty-three freshmen. Curriculum covers algebra, geometry (Legendre), trigonometry, analytic geometry and calculus.

1863. Professor Edward Olney and an instructor do the teaching.

1877. There is a staff of five. Curriculum expands slightly, with encouragement to those who wish to study topics such as quaternions, calculus of variations, calculus of finite differences.

1881. A complete set of Crelle's Journal is donated to the tiny University Library.

1887. There are courses on projective geometry and theory of functions, including elliptic functions.

1888. Alexander Ziwet and Frank N. Cole join the department. Ziwet remained until 1925 and was a major influence through his courses, donation of many books to the library and a generous bequest, which funds the Ziwet lectures. Cole left in 1895. While at Michigan, he wrote papers on group theory and had as a student and colleague G. A. Miller, who published many papers on group theory. Both Ziwet and Cole were much involved with formation of the American Mathematical Society (AMS), of which Cole was secretary from 1896 to 1920. The department's Mathematics Club began before 1891 in Ziwet's parlor.

1895. James W. Glover joins the department, remaining until 1937. He developed a strong program in actuarial mathematics. He served as chair from 1926 until 1934.

1900. Walter B. Ford joins the department. He wrote on asymptotic series and summability theory, wrote textbooks and strengthened the curriculum. He was active in the AMS and the Mathematical Association of America (MAA), of which he was President in 1927-1928. He became very wealthy through investments and made gifts to the MAA; his son later gave a large sum to the MAA to create the Walter B. Ford Lecture Fund.

1901. Beginning of a separation of mathematics instruction for engineering students, with Alexander Ziwet in charge. This lasted until 1928 and led to mathematics office in successive engineering buildings.

1908. The department has grown to twenty. The curriculum includes Fourier series and spherical harmonics, ordinary and partial differential equations, theory of substitutions, theory of numbers, theory of invariants, potential theory, courses for teachers.

1909. Theophil H. Hildebrandt joins the department, to remain until 1957, serving as chair from 1934 to 1957. He was a student of E. H. Moore in Chicago and did important work in functional analysis and integration theory. In 1923 he gave the first general proof of the principle of uniform boundedness for Banach spaces and in 1928 he published a basic paper on the spectral theory of compact operators. He was the first recipient of the Chauvenet Prize of the MAA and was President of the AMS in 1945-1946. He is honored by the T. H. Hildebrandt Assistant Professorships in the department.

1911. First Ph. D. granted in the department. The recipient was W. O. Mendenhall, who wrote on divergent series under Ford. By 1941, ninety Ph.D.s had been granted and since then an average of about 10 a year have received the degree.

1916. Harry Carver joins the department, to remain until 1961. He had a major influence on the field of statistics; he personally started the Annals of Mathematical Statistics and had a leading part in the founding of the Institute of Mathematical Statistics.

1920. The curriculum expands to include courses in applied mathematics: vector analysis, hydrodynamics, elasticity, celestial mechanics; also courses in infinite series and products, divergent series, history of mathematics, graphical methods.

1922. Ruel V. Churchill joins the department, to remain until 1966. He did much for the applied mathematics program and had wide influence through his books on applied analysis.

1926. George Y. Rainich and Raymond L. Wilder join the department, to remain until 1956 and 1968 respectively. Both did much to strengthen the department in many ways: in particular, by introduction of more seminars and colloquia. Rainich wrote on relativity theory and differential geometry, Wilder was an outstanding topologist, author of "Topology of Manifolds" (AMS Colloquium Publication), had many Ph. D. students. He was President of the AMS in 1955-1956 and of the MAA in 1965-1966. Rainich ran an "orientation seminar" for graduate students and thereby encouraged many to follow fruitful careers in mathematics. Wilder was active in at least one `secret' group organized to discuss current research. He and W. L. Ayres, who was in the department from 1929 to 1941, ran a 2-week Topology Congress in June of 1940, which led to an important publication (it was this Congress which brought me to Ann Arbor—I had no job at the time and was offered one by Hildebrandt during the Congress, at which I had presented a paper.)

1930-1940. The following entered the department: Robert C. F. Bartels in applied mathematics, who later became the first director of the University's Computing Center; Herman H. Goldstine, in functional analysis, who later worked with von Neumann in developing the digital computer; Sumner B. Myers, in differential geometry and functional analysis; Cecil J. Nesbitt in algebra and actuarial mathematics (a field in which he had major influence), Robert M. Thrall in algebra.

1940-1945. The years of World War II had a major impact on the University. Enrollments were greatly reduced and some faculty took leave for military research. There were some military training programs on campus. (We taught some V-12 Navy students and some Air Force officers preparing to be meteorologists; the latter program is reported to have trained some 10,000 officers, when at most 1000 were needed, all because of a misplaced 0.) Several persons joined the department: George E. Hay in applied mathematics, who later became chair in 1957-1967; Erich Rothe, in functional analysis; Samuel Eilenberg and Norman Steenrod, who made major contributions to topology.

In 1940 there were 35 staff members. The number increased to 84 in 1965 and decreased soon thereafter because of transfer of some staff to computer science and formation of a separate Statistics Department in 1969.

1945-1950. Richard Brauer in algebra, William J. LeVeque in number theory, George Piranian and Maxwell Reade in complex analysis, Phillip Jones in history of mathematics and Hans Samelson, in topology and geometry, enter the department. LeVeque was chair from 1967 to 1970.

1950-1960. Fred Gehring, in complex analysis, Lamberto Cesari, in calculus of variations, Roger C. Lyndon, in algebra, join the department. In 1952 the Michigan Mathematical Journal is initiated, under the leadership of Rainich, who became excited about "desktop publishing". In 1953 the department sponsors a 2-week conference on complex analysis, attended by major figures in this field and a publication results. H. Chandler Davis, a member of the department, is forced to leave in 1955 because of refusal to answer questions of a Congressional subcommittee on "un-American" activities. (The University is subsequently censured by AAUP for this action, and the whole episode is recalled annually at the Senate Lecture on Academic and Intellectual Freedom.)

1960-1991. A number of distinguished mathematicians (too many to name) join the department. There are many special conferences and invited lectures. Digital computing affects courses, research, departmental operations. The Engineering College moves to North Campus, increasing the difficulty in coordination of instruction with the department.

Departmental Buildings from 1940 on. In 1940 there were math. faculty offices in Angell Hall and a few in West Engineering Building (now West Hall), an old East Hall (an old schoolhouse, which stood just north of present East Hall), and East Engineering Building (now East Hall). The desire to unite the department led to creation of building committees. I served on one in the 1960's. Encouragement by the University administration led our committee to working with the University architect to develop detailed plans. About 1965 the Michigan Legislature passed a bill requiring approval of such plans and of the architect chosen by a Legislative Committee. President Hatcher resisted this action as a violation of autonomy granted to the University in the Michigan Constitution and a lawsuit was filed. The Legislature responded by denying building funds to the University. Thus our projected new mathematics building was cancelled. Eventually President Fleming saw the light and told the Legislature that the University would accept their requirements and, since then, the funds have flowed (as is evident to all).

### The Department of Mathematics—An Encyclopedic Survey, Part IV (PDF)

pp. 644-657, The University of Michigan Press, Ann Arbor, 1944, by John W. Bradshaw, James W. Glover, and Harry C. Carver.

### The Department of Mathematics—An Encyclopedic Survey, Part VI (PDF)

1940-1975, pp. 183-187, Bentley Historical Library, The University of Michigan, Ann Arbor, 1981, by Phillip S. Jones.

### Mathematics at the University of Michigan (PDF)

by Wilfred Kaplan, in A Century of Mathematics in America, Part 3 (Peter Duren, ed.), pp. 179-189, American Mathematical Society, Providence, RI, 1989.

### Reminiscences of Mathematics at Michigan (PDF)

by Raymond Wilder, in A Century of Mathematics in America, Part 3 (Peter Duren, ed.), pp. 191-204, American Mathematical Society, Providence, RI, 1989.

### The Purge (PDF)

by Chandler Davis, in A Century of Mathematics in America, Part 1 (Peter Duren, ed.), pp. 413-428, American Mathematical Society, Providence, RI, 1988.

### Biographical Memoir of Raymond Louis Wilder

by Frank Raymond, Biographical Memoirs, Volume 82, The National Academy Press, Washington, DC, 2002.