Paul Shaman delves into the history of the Putnam Mathematics Competition, and some of its notable laureates. He writes:
The William Lowell Putnam Mathematics Competition is held annually. Undergraduates at schools in the US and Canada are eligible, and many of those who do well go on to have distinguished careers in the mathematical sciences and other fields. In addition to the competition between individuals, there is a team contest among schools, with three people on a team. Since 1962, the examination has involved a three-hour morning session and a three-hour afternoon session, each with six questions. The top five individual performers are designated Putnam Fellows and receive monetary awards. The top teams are also awarded monetary prizes. Originally three teams received the prizes, and later the awards were expanded to four teams, and then to the current five. Several of the Putnam Fellows went on to become Fields Medalists, and two received the Nobel Prize in Physics.
Over the history of the competition, many entrants who achieved strong performances and were on winning teams went to become prominent statisticians and probabilists. For statisticians and probabilists, two Putnam outcomes are notable. In the February 1958 competition, three of the five Putnam Fellows subsequently became leading researchers in statistics and probability. They were David Brillinger, University of Toronto; Richard Dudley, Harvard; and Lawrence Shepp, Polytechnic Institute of Brooklyn. In addition, Edward L. Kaplan was a Putnam Fellow for three consecutive years, 1939–1941, while a student at Carnegie Institute of Technology.
Currently, Putnam Fellows are awarded \$2,500; lesser amounts to other top finishers. The department of the top team is awarded \$25,000, and each team member receives \$1,000. In the February 1958 competition, these awards were \$50, \$400, and \$40, respectively.
The Putnam Competition is underwritten by a trust established by Elizabeth Lowell Putnam in her will, written in 1927, to honor her late husband, William Lowell Putnam, a member of the Harvard class of 1882 and a prominent lawyer and banker. Mrs. Putnam’s intent was to sponsor intellectual competition among schools as had been advocated by her husband. After Mrs. Putnam died in 1935, her sons consulted with George David Birkhoff and Garrett Birkhoff of the Harvard Mathematics Department, both friends of the Putnam family, as to the use of her bequest. The structure of the Competition was formulated, with the Mathematical Association of America in charge of administration, and the first examination took place in 1938. With several exceptions, the examination has been given annually. There was a three-year hiatus during World War II, and two examinations were held in 1958. Now the Competition is staged on the first Saturday in December. Birkhoff (1965) and Bush (1965) describe the history of events leading to the Competition and the early years.
In the first eight years of the Competition, Toronto fielded the top-ranked team four times and Brooklyn College three times. Over the history of the Competition, Harvard has had the greatest number of first place team finishes, with Caltech second and MIT third. See Gallian (2004, 2014) for a detailed accounting of the Putnam results. Additional information is given in the Wikipedia article.
Table 1, below, lists the Putnam Fellows who became active in statistics and probability, with their undergraduate institutions. Their doctoral degree information is given in Table 2. J. Arthur Greenwood earned the first doctorate awarded by Harvard’s Department of Statistics.
For each Putnam Competition, the results, including the questions and their solutions, are reported subsequently in The American Mathematical Monthly. In addition to the Putnam Fellows, top team performances, and those individuals receiving honorable mention and above are cited. Tables 3 and 4 list such performances by persons who have contributed to research in statistics and probability.
Table 1. Putnam Fellows and their Undergraduate Institutions
Name | Years | Institution |
Edward L. Kaplan | 1939, 1940, 1941 | Carnegie Institute of Technology |
Donald A. S. Fraser | 1946 | University of Toronto |
J. Arthur Greenwood | 1946 | Harvard |
Arthur P. Dempster | 1951 | University of Toronto |
David R. Brillinger | S1958 | University of Toronto |
Richard M. Dudley | S1958 | Harvard |
Lawrence A. Shepp | S1958 | Polytechnic Institute of Brooklyn |
Louis Jaeckel | 1960 | UCLA |
Theodore C. Chang | 1966 | MIT |
Russell D. Lyons | 1977, 1978 | Case Western Reserve University |
Robin Pemantle | 1981 | University of California Berkeley |
Martin V. Hildebrand | 1985 | Williams College |
John S. Tillinghast | 1987 | University of California Davis |
Table 2. Putnam Fellows and their Doctoral Institutions and Advisers
Name | Year | Institution | Advisers |
Edward L. Kaplan | 1951 | Princeton | John W. Tukey |
Donald A. S. Fraser | 1949 | Princeton | John W. Tukey and Samuel S. Wilks |
J. Arthur Greenwood | 1959 | Harvard | Frederick Mosteller and John W. Pratt |
Arthur P. Dempster | 1956 | Princeton | John W. Tukey |
David R. Brillinger | 1961 | Princeton | John W. Tukey |
Richard M. Dudley | 1962 | Princeton | Gilbert A. Hunt and J. Edward Nelson |
Lawrence A. Shepp | 1961 | Princeton | William Feller |
Louis Jaeckel | 1969 | UC Berkeley | Erich L. Lehmann |
Theodore C. Chang | 1972 | UC Berkeley | Wu-Yi Hsiang |
Russell D. Lyons | 1983 | Michigan, Ann Arbor | Hugh L. Montgomery and Allen L. Shields |
Robin Pemantle | 1988 | MIT | Persi Diaconis |
Martin V. Hildebrand | 1990 | Harvard | Persi Diaconis |
Table 3. Members of Winning Teams
Name | Year | Institution | Team rank |
Herman Chernoff | 1942 | CCNY | 4 |
Donald A. S. Fraser | 1946 | Toronto | 1 |
Julian Keilson | 1946 | Brooklyn College | 3 |
Hale F. Trotter | 1952 | Queen’s University | 1 |
Charles J. Stone | 1957 | Caltech | 4 |
Lawrence A. Shepp | S1958 | Brooklyn Poly | 1 |
David R. Brillinger | S1958 | Toronto | 3 |
Richard M. Dudley | F1958 | Harvard | 1 |
David R. Brillinger | F1958 | Toronto | 2 |
Theodore C. Chang | 1966 | MIT | 2 |
Michael Klass | 1968 | UCLA | 3 |
Richard Arratia | 1971 | MIT | 5 |
Russell D. Lyons | 1976 | CWRU | 4 |
Russell D. Lyons | 1978 | CWRU | 1 |
Robin Pemantle | 1980 | UC Berkeley | 5 |
Table 4. Honorable Mention and Above
Name | Institution | Year and rank range |
Julian Keilson | Brooklyn College | 1946, 11–15; 1947, 6–10 |
Hale F. Trotter | Queen’s University | 1951, 12–20; 1952, 6–10 |
Arthur P. Dempster | Toronto | 1952, 6–10 |
Gian Carlo Rota | Princeton | 1953, 11–25 |
Lawrence A. Shepp | Brooklyn Poly | 1957, 6–11 |
Richard M. Dudley | Harvard | F1958, 6–10 |
Stanley A. Sawyer | Caltech | 1959, 11–28 |
Fred L. Bookstein | University of Michigan | 1964, 12–35; 1965, 12–35 |
Theodore C. Chang | MIT | 1965, 12–35 |
Richard Arratia | MIT | 1968, 13–35; 1971, 11–42 |
James A. Reeds | University of Michigan | 1968, 13–35 |
Russell D. Lyons | Case Western Reserve University | 1975, 11–40; 1976, 12–40 |
Neal Madras | McGill | 1977, 11–39; 1978, 11–42 |
Kenneth S. Alexander | University of Washington | 1978, 11–42 |
Robin Pemantle | UC Berkeley | 1980, 11–43; 1982, 6–11 |
Robert Shapire | Brown | 1985, 11–44 |
John S. Tillinghast | UC Davis | 1988, 12–49 |
Tong Zhang | Cornell | 1992, 6–11; 1993, 29–57 |
This post was edited 28 June 2021 to include Russell D. Lyons.
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References
Birkhoff, G. (1965). The William Lowell Putnam Mathematical Competition: Early history. Amer. Math. Monthly, Vol. 72, pp. 469–473
Bush, L. E. (1965). The William Lowell Putnam Competition: Later history and summary of Results. Amer. Math. Monthly, Vol. 72, pp. 474–483
Gallian, J. A. (2004). The first sixty-six years of the Putnam Competition. Amer. Math. Monthly, Vol. 111, pp. 691–699
Gallian, J. A. (2014). The Putnam Competition from 1938–2014. www.d.umn.edu/~jgallian/putnam14.pdf
William Lowell Putnam Mathematical Competition. https://en.wikipedia.org/wiki/William_Lowell_Putnam_Mathematical_Competition
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