Aug 28, 2015

Putnam Mathematics Competition

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
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
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
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
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



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.
William Lowell Putnam Mathematical Competition.


  • I wonder how accurate this is; I’m missing in all four tables.

    • Hello Russell. Sorry about missing you off! Can you email me the details ( and I’ll edit the article and notify Paul Shaman. Best wishes, Tati

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