Mathematics

Mathematics has been prominent in the Princeton curriculum since the founding of the College. In 1760, entering students were required to have an understanding of the rules of arithmetic, and underclassmen learned algebra, trigonometry, geometry, and conic sections. In 1853 a Boston newspaper reported that at Princeton the study of mathematics was carried on ``to an extent not excelled by any other college in the country.'' In the early years, instruction in mathematics was given by faculty members who generally taught other subjects as well. The first trained mathematician on the faculty was Walter Minto, who had studied in Pisa and had taught in Edinburgh before being called to Princeton in 1787. Not until a century later did the College again have on its faculty teachers who had studied in the European mathematical centers; the first was Henry Burchard Fine (A.B. Princeton 1880), who received his Ph.D. degree at Leipzig in 1885.

The state of mathematics in Princeton changed dramatically after 1905; the beginning of the development of Princeton as one of the world's great centers of mathematical teaching and research took place that year, and was primarily due to Henry Burchard Fine. Fine had been appointed dean of the faculty by President Woodrow Wilson in 1903; and when the University was organized into academic departments in 1904 he was also appointed the first chairman of the Department of Mathematics. In 1905 Fine persuaded Wilson to extend the new preceptorial system to include mathematics and to appoint as preceptors a very promising group of young mathematicians, including Luther P. Eisenhart, who had come to Princeton as an instructor in 1900 and became a distinguished differential geometer, and Oswald Veblen, a geometer and later a mathematical statesman. Dean Fine's ability to detect mathematical talent is evidenced by even a partial list of other appointments he made to the Princeton faculty: James Jeans, Professor of Applied Mathematics, who shortly returned to Cambridge University; George David Birkhoff, who later became the leading mathematical figure at Harvard; J.H.M. Wedderburn, an algebraist whose name is familiar to all mathematicians; James W. Alexander II (B.S. Princeton 1910, Ph.D. 1915), the topologist; and Solomon Lefschetz, the algebraic geometer and topologist. These appointments produced a mathematics faculty of the first rank during the 1920s, and an atmosphere of freshness and enthusiasm that lured a great many of the ablest young mathematicians to postgraduate study at Princeton as National Research Fellows. The publication of the Annals of Mathematics was taken over from Harvard in 1911; and under the direction of Wedderburn and Lefschetz (successively chief editors of that journal for over forty years) the Annals became one of the principal journals of research mathematics in the world.

During this period, mathematics in Princeton, and indeed throughout the United States, was still under a severe handicap in comparison with mathematics in the great European centers. All of the mathematicians in this country were primarily teachers; faculties were small, and the teaching loads, consisting mainly of rather routine courses, were heavy. In Europe by contrast there were forty or fifty posts that were essentially research professorships of mathematics, with limited teaching duties and considerable prestige. The situation changed in 1928, when Princeton instituted the scientific research fund, which made possible a stream of distinguished visiting mathematicians such as G. H. Hardy and P.A.M. Dirac of Cambridge and P. A. Alexandroff of Moscow. At that time too Princeton established the first research professorship in mathematics in the United States, the Henry Burchard Fine Professorship, a gift of Thomas D. Jones 1876. In addition, Jones and his niece Gwethalyn Jones endowed a memorial building to honor Dean Fine, who died in 1928. This building, dedicated in 1931, was commodious and elegant, with handsome wood-panelled library, common rooms, and faculty studies; it housed the department in comfort and style for almost forty years, and Fine Hall became synonymous with the Princeton Department of Mathematics.

Mathematical research in the United States was further advanced when the Institute for Advanced Study was founded in Princeton in 1930. Although the Institute and the University are separate institutions, they have had close and productive relations from the beginning. The School of Mathematics was the first branch of the Institute to be staffed in 1932, and had temporary quarters in Fine Hall until 1939. Two of the Institute's first five professors, Alexander and Veblen, had been at the University for many years, John von Neumann had been professor of mathematical physics since 1930, and Hermann Weyl had been the Thomas D. Jones Professor of Mathematical Physics at Princeton in 1928-1929. Only Einstein had never held a position at the University, although he had delivered a series of lectures there on the theory of relativity in 1921. The Institute joined the University in the publication of the Annals of Mathematics, and in the founding of the Princeton Mathematics Series (1939) and the Annals of Mathematics Studies (1940), both of which were originated and edited for many years by Albert W. Tucker and continue to be published by Princeton University Press.

Under the chairmanship, from 1929 to 1945, of Fine's successor, Luther P. Eisenhart, the department continued to make outstanding appointments of promising young mathematicians, such as Alonzo Church, a noted logician; Eugene P. Wigner, Thomas D. Jones Professor of Mathematical Physics and later a Nobel laureate; Salomon Bochner, known for the breadth of his contributions to many different areas of analysis; and Samuel S. Wilks, a distinguished mathematical statistician. With the permanent mathematical faculties and visiting members of the University and the Institute, Princeton became an intensely active center for mathematical research in the 1930s. Reporting on an International Congress of Mathematicians held in Oslo in 1936, a Norwegian newspaper ran this headline: ``Princeton is the mathematical center of the world but at the moment it is in Oslo.''

During the 1920s and 1930s Princeton's uniquely successful graduate program in mathematics also developed. For two decades after 1935, Princeton produced more Ph.D. degrees in mathematics than any other American university, and an American Mathematical Society study in 1974 showed that the Princeton graduate program is by far the largest producer of the tenured faculty members in the country's leading mathematics departments. The characteristic aspects of the Princeton Ph.D. program in mathematics are freedom from formal course requirements, an emphasis on original research at an early stage of the student's education, and a spirit of cooperative study and research in which the students and faculty participate jointly.

Political developments in Europe in the 1930s increased the flow of talented refugees to the United States, and the University and the Institute helped to channel many mathematicians to positions in this country. This vast influx of talent altered the mathematical balance of the world, and finally raised American mathematics to the level of that of the older centers of research in Europe. The first postwar international gathering of mathematicians -- over a hundred leaders from nine nations -- took place in Fine Hall in 1946, as part of Princeton's bicentennial celebration. The greater amount of mathematical teaching and research required in the more technologically oriented postwar world led to an increase in the size of the faculty. Among those added to the faculty during Solomon Lefschetz's chairmanship, from 1945 to 1953, were Ralph Fox and Norman Steenrod in topology; Emil Artin in algebra; John Tukey in mathematical statistics; Valentine Bargmann and Arthur Wightman in mathematical physics; William Feller in probability; and Donald C. Spencer in analysis.

Lefschetz was succeeded as chairman by Albert W. Tucker, who served from 1953 to 1963. Thereafter the character of the departmental administration changed to a more cooperative undertaking. with duties shared by almost the entire senior faculty; John W. Milnor, Gilbert A. Hunt, Elias M. Stein, William Browder, Joseph J. Kohn, and Robert C. Gunning served successive short terms as chairmen after 1963. Milnor (Princeton A.B. 1951, Ph.D. 1954, winner of the Madison medal, 1977), who had written his first published paper as a freshman, was promoted to full professor in 1960, the youngest in 50 years. He became a professor at the Institute for Advanced Study in 1969. His age record for professorial precocity was broken by Charles L. Fefferman (Princeton Ph.D. 1969), who became full professor of mathematics at the University of Chicago in 1971, and a year later, at the age of twenty-three, was elected by the trustees to a professorship at Princeton, thus equaling a record set a century and a half earlier by another professor of mathematics, John Maclean, later president of the College. These and other appointments during this period gave Princeton a strong faculty in topology (traditionally an area of excellence at Princeton), in algebraic number theory and algebraic geometry, in various branches of analysis (Fourier analysis, partial differential equations, complex analysis, probability), and in mathematical physics (a unique interdepartmental program).

During the 1950s and 1960s the heightened national interest in science and mathematics following Sputnik and the space program led to a further expansion of the department. The number of graduate students increased considerably, with generous support through the National Science Foundation and Woodrow Wilson Foundation Fellowships; undergraduate majors increased from a handful to over two dozen each year; and by the mid-sixties the faculty had more than doubled since the war. Altogether, the department was nearly five times larger than when it had moved into Fine Hall in 1931, so that that elegant building was no longer large enough. A new building, adjacent to the new physics building, was erected in 1969 to house the Department of Mathematics and the new Department of Statistics, which had separated from the Mathematics Department in 1965 under the chairmanship of John W. Tukey. The new building, with a tower containing faculty studies, a large underground library, and extensive study areas, was a sharp contrast to the old building; but to mark fittingly the continuity of what had by now become the distinguished tradition of Princeton mathematics, the name Fine Hall was transferred to the new building, and the old one renamed Jones Hall in honor of the original donors. The Department has continued to flourish in its new quarters, and to uphold its reputation as a world center for teaching and research in mathematics.

Robert C. Gunning


From Alexander Leitch, A Princeton Companion, copyright Princeton University Press (1978).

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