william lowell putnam mathematical competition

The William Lowell Putnam Mathematical Competition, often abbreviated to Putnam Competition, is an annual mathematics competition for undergraduate college students, awarding scholarships and cash prizes ranging from $2,500 to $250 for the top students and $25,000 to $5,000 for the top schools. The competition was funded in 1927 by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam (Harvard 1882), who while alive was an advocate of intercollegiate intellectual competition. The exam has been offered annually since 1938 and is administered by the Mathematical Association of America.

The competition today

The Putnam competition now takes place on the first Saturday in December, and consists of two three-hour sittings and a lunch break. Each competitor attempts to solve twelve problems, nearly all mathematical proofs, which can typically be solved with only basic knowledge of college mathematics but which require extensive creative thinking. Each of the twelve questions is worth any amount from 1 to 10 points, but the most frequent scores above zero are 10 points, for a complete solution; 9 points, for a nearly complete solution; and 1 point, for the beginnings of a solution. The examination is considered to be very difficult: it is typically attempted by students specializing in mathematics, but the median score is usually one or two points out of 120 possible, and perfect scores are exceptionally rare. In 2003, of the 3615 students taking the exam, 1024 (28%) scored 10 or more points, and 42 points was sufficient to make the top 102. At a participating college, as many students as wish to take part in the exam may enter; but the school's official team consists of three individuals whom it designates in advance. Team scoring is analogous to that used in cross-country running; a team's score is the sum of the ranks of its three team members, with the lowest team score winning. It is entirely possible, even commonplace at some institutions, for the eventual results to show that the "wrong" team was picked — i.e., that some students not on the official team outscored the official team members. The top five teams win $25,000, $20,000, $15,000, $10,000, and $5,000 respectively, with $1,000, $800, $600, $400, and $200 for team members. The top five individual scorers are named Putnam Fellows and awarded $2,500. One of them is also awarded the William Lowell Putnam Prize Scholarship of $12,000 plus tuition for graduate study at Harvard University. Sixth through 15th place individuals receive $1,000 and the next ten receive $250. The names of the top 100 students are published in American Mathematical Monthly. In December 2003 the examination was taken by 3615 students from 479 colleges. The 2004 examination was held on December 4. Many contestants have gone on to become distinguished researchers in mathematics and other fields. A number of them have received the Fields Medal or the Nobel Prize in Physics.

Winners

Top-scoring teams

Since the second competition in 1939, competing teams have been ranked.

Year	First	Second	Third	Fourth	Fifth
1938	(teams were not ranked)
1939	Brooklyn College	MIT	Mississippi Woman's College
1940	Toronto	Yale	Columbia
1941	Brooklyn College	UPenn	MIT
1942	Toronto	Yale	MIT	City College of New York
1946	Toronto	MIT	Brooklyn College	Carnegie Institute of Technology
1947	Harvard	Yale	Columbia	UPenn
1948	Brooklyn College	Toronto	Harvard	City College of New York (tie) McGill
1949	Harvard	Toronto	Carnegie Institute of Technology	City College of New York
1950	Caltech	Harvard	New York University (NYU)	Toronto
1951	Cornell	Harvard	Cooper Union	City College of New York
1952	Queen's University	Polytechnic Institute of Brooklyn	Harvard	MIT
1953	Harvard	City College of New York	Cornell	UC Berkeley
1954	Cornell	Harvard	MIT	Toronto
1955	Harvard	Toronto	Yale	Kenyon
1956	Harvard	Columbia	Queen's University	MIT
1957	Harvard	Columbia	Cornell	Caltech
Spring 1958	Polytechnic Institute of Brooklyn	Harvard	Toronto	University of Manitoba
Fall 1958	Harvard	Toronto	Caltech	Cornell
1959	Polytechnic Institute of Brooklyn	Caltech	Toronto	Harvard	Case Western Reserve
1960	UC Berkeley	Harvard	MIT	Michigan State	Cornell
1961	Michigan State	MIT	Caltech	Harvard	Dartmouth
1962	Caltech	Dartmouth	Harvard	Queen's University	UCLA
1963	Michigan State	Brooklyn College	UPenn	Caltech	MIT
1964	Caltech	MIT	Harvard	Case Western Reserve	UC Berkeley
1965	Harvard	MIT	Toronto	Princeton	Caltech
1966	Harvard	MIT	Chicago	Michigan	Princeton
1967	Michigan State	Caltech	Harvard	MIT	Michigan
1968	MIT	Waterloo	UCLA	Michigan State	Kansas
1969	MIT	Rice	Chicago	Harvard	Yale
1970	Chicago	MIT	Toronto	Illinois Institute of Technology	Caltech
1971	Caltech	Chicago	Harvard	UC Davis	MIT
1972	Caltech	Oberlin	Harvard	Swarthmore	MIT
1973	Caltech	University of British Columbia	Chicago	Harvard	Princeton
1974	Waterloo	Chicago	Caltech	MIT	University of British Columbia
1975	Caltech	Chicago	MIT	Princeton	Harvard
1976	Caltech	Washington University in St. Louis	Princeton	Case Western Reserve (tie) MIT
1977	Washington University in St. Louis	UC Davis	Caltech	Princeton	MIT
1978	Case Western Reserve	Washington University in St. Louis	Waterloo	Harvard	Caltech
1979	MIT	Caltech	Princeton	Stanford	Waterloo
1980	Washington University in St. Louis	Harvard	Maryland, College Park	Chicago	UC Berkeley
1981	Washington University in St. Louis	Princeton	Harvard	Stanford	Maryland, College Park
1982	Harvard	Waterloo	Caltech	Yale	Princeton
1983	Caltech	Washington University in St. Louis	Waterloo	Princeton	Chicago
1984	UC Davis (tie) Washington University in St. Louis		Harvard	Princeton	Yale
1985	Harvard	Princeton	UC Berkeley	Rice	Waterloo
1986	Harvard	Washington University in St. Louis	UC Berkeley	Yale	MIT
1987	Harvard	Princeton	Carnegie Mellon	UC Berkeley	MIT
1988	Harvard	Princeton	Rice	Waterloo	Caltech
1989	Harvard	Princeton	Waterloo	Yale	Rice
1990	Harvard	Duke	Waterloo	Yale	Washington University in St. Louis
1991	Harvard	Waterloo	Harvey Mudd	Stanford	Yale
1992	Harvard	Toronto	Waterloo	Princeton	Cornell
1993	Duke	Harvard	Miami University	MIT	Michigan
1994	Harvard	Cornell	MIT	Princeton	Waterloo
1995	Harvard	Cornell	MIT	Toronto	Princeton
1996	Duke	Princeton	Harvard	Washington University in St. Louis	Caltech
1997	Harvard	Duke	Princeton	MIT	Washington University in St. Louis
1998	Harvard	MIT	Princeton	Caltech	Waterloo
1999	Waterloo	Harvard	Duke	Michigan	Chicago
2000	Duke	MIT	Harvard	Caltech	Toronto
2001	Harvard	MIT	Duke	UC Berkeley	Stanford
2002	Harvard	Princeton	Duke	UC Berkeley	Stanford
2003	MIT	Harvard	Duke	Caltech	Harvey Mudd
2004	MIT	Princeton	Duke	Waterloo	Caltech

Teams ranked by historical performance

Below is a table of teams by the number of appearances in the top five and number of titles. Where multiple teams have the same number of appearances in the top five, they are ranked by number of championships, and then listed in alphabetical order. While some may see this as a rough gauge of the level of the undergraduate mathematical programs at various institutions, a number of factors militate against this assumption:

Some institutions have participated for many years while others are relative latecomers.
Some university teams actively train for the competition with faculty help and reference to past years' questions; at others, there is a student club which practices — but at many institutions, there is no formal preparation at all.
As described earlier in this article, it is possible for the official members of a team to not score as highly as others from the same university who have not been designated members of the official team.
Finally, and most importantly, "contest math" is seen by many as quite different from original mathematical research — the real aim of university math departments — and is not necessarily the best predictor of it.

Top five finishes (as of 2004 competition)	Team
50	Harvard
35	MIT
28	Caltech
23	Princeton
16	Toronto, Waterloo
11	Washington University in St. Louis, Yale
10	Chicago, Duke
9	UC Berkeley, Cornell
5	Brooklyn College, City College of New York, Michigan State, Stanford
4	Case Western Reserve, Columbia, Michigan, Rice
3	Polytechnic Institute of Brooklyn, UC Davis, Queen's University, Carnegie Mellon (formerly Carnegie Institute of Technology), UPenn
2	Dartmouth, Harvey Mudd, Maryland, College Park, UCLA, University of British Columbia
1	Cooper Union, Illinois Institute of Technology, Kansas, Kenyon, McGill, Miami University, Mississippi Woman's College, New York University, Oberlin, Swarthmore, University of Manitoba

First place finishes (as of 2004 competition)	Team
24	Harvard
9	Caltech
5	MIT
4	Washington University in St. Louis
3	Brooklyn College, Duke, Michigan State, Toronto
2	Cornell, Polytechnic Institute of Brooklyn, Waterloo
1	UC Berkeley, UC Davis, Case Western Reserve, Chicago, Queen's University

Putnam Fellows

Since the first competition, the top five scorers on the examination have been named Putnam Fellows. Within the top five, Putnam fellows are not ranked. Only five students have been Putnam fellows four times: Dan Coppersmith (1968-71), Bjorn M. Poonen (1985-88), Ravi D. Vakil (1988-91), Gabriel D. Carroll (2000-03), and Reid W. Barton (2001-04). Sixteen others have won the award three times. The following table lists all Putnam fellows from 1938 to present, with the years they placed in the top five.

George W. Mackey (Rice)	1938
Irving Kaplansky (Toronto)	1938
Michael J. Norris (College of St. Thomas)	1938
Robert W. Gibson (Fort Hays Kansas State College)	1938
Bernard Sherman (Brooklyn College)	1938, 1939
Abraham Hillman (Brooklyn College)	1939
Richard P. Feynman (MIT)	1939
William Nierenberg (City College of New York)	1939
Edward L. Kaplan (Carnegie Institute of Technology)	1939, 1940, 1941
John Cotton Maynard (Toronto)	1940
Robert Maughan Snow (George Washington University)	1940
W. J. R. Crosby (Toronto)	1940
Andrew M. Gleason (Yale)	1940, 1941, 1942
Paul C. Rosenbloom (Penn)	1941
Richard F. Arens (UCLA)	1941
Samuel I. Askovitz (Penn)	1941
Harold Victor Lyons (Toronto)	1942
Harvey Cohn (City College of New York)	1942
Melvin A. Preston (Toronto)	1942
Warren S. Loud (MIT)	1942
Donald A. Fraser (Toronto)	1946
Eugenio Calabi (MIT)	1946
Felix Browder (MIT)	1946
J. Arthur Greenwood (Harvard)	1946
Maxwell A. Rosenlicht (Columbia)	1946, 1947
Clarence Wilson Hewlett, Jr. (Harvard)	1947
William Turanski (Penn)	1947
Eoin L. Whitney (University of Alberta)	1947, 1948
W. Forrest Stinespring (Harvard)	1947, 1949
George F. D. Duff (Toronto)	1948
Harry Gonshor (McGill)	1948
Leonard Geller (Brooklyn College)	1948
Robert L. Mills (Columbia)	1948
Donald J. Newman (City College of New York)	1948, 1949, 1950
Ariel Zemach (Harvard)	1949
David L. Yarmush (Harvard)	1949
J. W. Milnor (Princeton)	1949, 1950
John P. Mayberry (Toronto)	1950
Richard J. Semple (Toronto)	1950
Z. Alexander Melzak (University of British Columbia)	1950
Arthur P. Dempster (Toronto)	1951
Harold Widom (City College of New York)	1951
Herbert C. Kranzer (New York University (NYU))	1951
Peter John Redmond (Cooper Union)	1951
James B. Herreshoff IV (UC Berkeley)	1951, 1952, 1953
Eugene R. Rodemich (Washington University, St. Louis)	1952
Gerhard Rayna (Harvard)	1952
Richard G. Swan (Princeton)	1952
Walter L. Bailey, Jr. (MIT)	1952
Marshall L. Freimer (Harvard)	1953
Norman Bauman (Harvard)	1953
Tai Tsun Wu (Minnesota)	1953
Samuel Jacob Klein (City College of New York)	1953, 1959, 1960
Benjamin Muckenhoupt (Harvard)	1954
James Daniel Bjorken (MIT)	1954
Leonard Evens (Cornell)	1954
William P. Hanf (UC Berkeley)	1954
Kenneth G. Wilson (Harvard)	1954, 1956
Howard C. Rumsey, Jr. (Caltech)	1955
Jack Towber (Brooklyn College)	1955
David B. Mumford (Harvard)	1955, 1956
Trevor Barker (Kenyon College)	1955, 1956
Everett C. Dade (Harvard)	1955, 1957
Richard Michael Friedberg (Harvard)	1956
David M. Bloom (Columbia)	1956, 1957
J. Ian Richards (Minnesota)	1957
Richard T. Bumby (MIT)	1957
Rohit J. Parikh (Harvard)	1957
David R. Brillinger (Toronto)	Spring 1958
Donald J. C. Bures (Queen's University)	Spring 1958
Lawrence A. Shepp (Polytechnic Institute of Brooklyn)	Spring 1958
Richard M. Dudley (Harvard)	Spring 1958
Joseph Lipman (Toronto)	Spring 1958, Fall 1958
Alan Gaisford Waterman (San Diego State College)	Fall 1958
John Rex Forrester Hewett (Toronto)	Fall 1958
Robert C. Hartshorne (Harvard)	Fall 1958
Alfred W. Hales (Caltech)	Fall 1958, 1959
Daniel G. Quillen (Harvard)	1959
Donald Passman (Polytechnic Institute of Brooklyn)	1959
Donald S. Gorman (Harvard)	1959
Martin Isaacs (Polytechnic Institute of Brooklyn)	1959
Stephen L. Adler (Harvard)	1959
Stephen Lichtenbaum (Harvard)	1959
Jon H. Folkman (UC Berkeley)	1960
Louis Jaeckel (UCLA)	1960
Melvin Hochster (Harvard)	1960
William R. Emerson (Caltech)	1960
Barry Wolk (University of Manitoba)	1961
Elwyn R. Berlekamp (MIT)	1961
Edward Anton Bender (Caltech)	1961, 1962
John Hathaway Lindsey (Caltech)	1961, 1962
William C. Waterhouse (Harvard)	1961, 1962
John William Wood (Harvard)	1962
Robert S. Strichartz (Dartmouth)	1962
Joel H. Spencer (MIT)	1963
Lawrence A. Zalcman (Dartmouth)	1963
Lawrence J. Corwin (Harvard)	1963
Robert E. Greene (Michigan State)	1963
Stephen E. Crick, Jr. (Michigan State)	1963
Barry B. MacKichan (Harvard)	1964
Fred William Roush (North Carolina)	1964
Roger E. Howe (Harvard)	1964
Rufus Bowen (UC Berkeley)	1964
Vern Sheridan Poythress (Caltech)	1964
Andreas R. Blass (University of Detroit)	1965
Barry Simon (Harvard)	1965
Daniel Fendel (Harvard)	1965
Lon M. Rosen (Toronto)	1965
Robert Bowen (UC Berkeley)	1965
Marshall W. Buck (Harvard)	1966
Robert E. Maas (Santa Clara)	1966
Robert S. Winternitz (MIT)	1966
Theodore C. Chang (MIT)	1966
Richard C. Schroeppel (MIT)	1966, 1967
David R. Haynor (Harvard)	1967
Dennis A. Hejhal (Chicago)	1967
Don B. Zagier (MIT)	1967
Peter L. Montgomery (UC Berkeley)	1967
Dean G. Huffman (Yale)	1968
Gerald S. Gras (MIT)	1968
Neal Koblitz (Harvard)	1968
Gerald A. Edgar (UC Santa Barbara)	1968, 1969
Don Coppersmith (MIT)	1968, 1969, 1970, 1971
Alan R. Beale (Rice)	1969
Steven Winkler (MIT)	1969
Robert A. Oliver (Chicago)	1969, 1970
Jeffrey Lagarias (MIT)	1970
Jockum Aniansson (Yale)	1970
Steven K. Winkler (MIT)	1970
Arthur Rubin (Purdue, Caltech)	1970, 1971, 1972
Dale Peterson (Yale)	1971
David Shucker (Swarthmore)	1971
Robert Israel (Chicago)	1971
Michael Yoder (Caltech)	1971, 1972
Arthur Rothstein (Reed College)	1972
David Vogan (Chicago)	1972
Dean Hickerson (UC Davis)	1972
Ira Gessel (Harvard)	1972
Angelos J. Tsirimokos (Princeton)	1973
Arthur L. Rubin (Caltech)	1973
Matthew L. Ginsberg (Wesleyan)	1973
Peter G. De Buda (Toronto)	1973
David J. Anick (MIT)	1973, 1975
Grant M. Roberts (Waterloo)	1974
James B. Saxe (Union)	1974
Karl C. Rubin (Princeton)	1974
Philip N. Strenski (Armstrong State)	1974
Thomas G. Goodwillie (Harvard)	1974, 1975
Ernest S. Davis (MIT)	1975
Franklin T. Adams (Chicago)	1975
Christopher L. Henley (Caltech)	1975, 1976
David J. Wright (Cornell)	1976
Nathaniel S. Kuhn (Harvard)	1976
Paul M. Herdig (Case Western Reserve)	1976
Philip I. Harrington (Washington University, St. Louis)	1976
Steven T. Tschantz (UC Berkeley)	1976, 1978
Adam L. Stephanides (Chicago)	1977
Michael Roberts (MIT)	1977
Paul A. Vojta (Minnesota-Minneapolis)	1977
Stephen W. Modzelewski (Harvard)	1977
Russell D. Lyons (Case Western Reserve)	1977, 1978
Mark R. Kleiman (Princeton)	1978
Peter W. Shor (Caltech)	1978
Randall L. Dougherty (UC Berkeley)	1978, 1979, 1980
Charles H. Walter (Princeton)	1979
Mark G. Pleszkoch (Virginia)	1979
Miller Puckette (MIT)	1979
Richard Mifflin (Rice University)	1979
Daniel J. Goldstein (Chicago)	1980
Laurence E. Penn (Harvard)	1980
Michael Raship (Harvard)	1980
Eric D. Carlson (Michigan State)	1980, 1982, 1983
Adam Stephanides (Chicago)	1981
Robin A. Pemantle (UC Berkeley)	1981
Scott R. Fluhrer (Case Western Reserve)	1981
David W. Ash (Waterloo)	1981, 1982, 1983
Michael J. Larsen (Harvard)	1981, 1983
Brian R. Hunt (Maryland, College Park)	1982
Edward A. Shpiz (Washington University, St. Louis)	1982
Noam D. Elkies (Columbia)	1982, 1983, 1984
Gregg N. Patruno (Princeton)	1983
Benji N. Fisher (Harvard)	1984
Daniel W. Johnson (Rose-Hulman)	1984
Richard A. Stong (Washington University, St. Louis)	1984
Michael Reid (Harvard)	1984, 1987
Everett W. Howe (Caltech)	1985
Keith A. Ramsay (Chicago)	1985
Martin V. Hildebrand (Williams)	1985
Douglas S. Jungreis (Harvard)	1985, 1986
Bjorn M. Poonen (Harvard)	1985, 1986, 1987, 1988
David J. Zuckerman (Harvard)	1986
Waldemar P. Horwat (MIT)	1986
David J. Grabiner (Princeton)	1986, 1987, 1988
David J. Moews (Harvard)	1986, 1987, 1988
Constantin S. Teleman (Harvard)	1987
John S. Tillinghast (UC Davis)	1987
Jeremy A. Kahn (Harvard)	1988
Ravi D. Vakil (Toronto)	1988, 1989, 1990, 1991
Andrew H. Kresch (Yale)	1989
Christo Athanasiadis (MIT)	1989
Colin M. Springer (Waterloo)	1989
Sihao Wu (Yale)	1989
William P. Cross (Caltech)	1989
Jordan Lampe (UC Berkeley)	1990
Raymond M. Sidney (Harvard)	1990
Eric K. Wepsic (Harvard)	1990, 1991
Jordan S. Ellenberg (Harvard)	1990, 1992
Joshua B. Fischman (Princeton)	1991
Xi Chen (Missouri-Rolla)	1991
Samuel A. Kutin (Harvard)	1991, 1992
Jeffrey M. Vanderkam (Duke)	1992
Serban M. Nacu (Harvard)	1992
Adam M. Logan (Princeton)	1992, 1993
Craig B. Gentry (Duke)	1993
Wei-Hwa Huang (Caltech)	1993
J. P. Grossman (Toronto)	1993, 1994, 1995
Kiran S. Kedlaya (Harvard)	1993, 1994, 1995
Lenhard L. Ng (Harvard)	1993, 1994, 1995
William R. Mann (Princeton)	1994
Jeremy L. Bem (Cornell)	1994, 1996
Sergey V. Levin (Harvard)	1995
Yevgeniy Dodis (NYU)	1995
Dragos N. Oprea (Harvard)	1996
Ioana Dumitriu (NYU)	1996
Robert D. Kleinberg (Cornell)	1996
Stephen S. Wang (Harvard)	1996
Daniel K. Schepler (Washington University, St. Louis)	1996, 1997
Ovidiu Savin (University of Pittsburgh)	1997
Patrick K. Corn (Harvard)	1997
Samuel Grushevsky (Harvard)	1997
Mike L. Develin (Harvard)	1997, 1998
Ciprian Manolescu (Harvard)	1997, 1998, 2000
Ari M. Turner (Princeton)	1998
Nathan G. Curtis (Duke)	1998
Kevin D. Lacker (Duke)	1998, 2001
Christopher C. Mihelich (Harvard)	1999
Colin A. Percival (Simon Fraser)	1999
Davesh Maulik (Harvard)	1999
Derek I.E. Kisman (Waterloo)	1999
Sabin Cautis (Waterloo)	1999
Abhinav Kumar (MIT)	1999, 2000
Pavlo Pylyavskyy (MIT)	2000
Alexander B. Schwartz (Harvard)	2000, 2002
Gabriel D. Carroll (UC Berkeley, Harvard)	2000, 2001, 2002, 2003
George Lee, Jr. (Harvard)	2001
Jan K. Siwanowicz (City University of New York)	2001
Reid W. Barton (MIT)	2001, 2002, 2003, 2004
Deniss Cebikins (MIT)	2002
Melanie E. Wood (Duke)	2002
Ralph C. Furmaniak (Waterloo)	2003
Ana Caraiani (Princeton)	2003, 2004
Daniel M. Kane (MIT)	2003, 2004
Vladimir V. Barzov (MIT)	2004
Aaron C. Pixton (Princeton)	2004

Elizabeth Lowell Putnam Award winners

Since 1992, the Elizabeth Lowell Putnam Award has been available to be awarded to a female participant with a high score. It is not awarded every year.

Dana Pascovici (Dartmouth)	1992
Ruth A. Britto-Pacumio (MIT)	1994
Ioana Dumitriu (NYU)	1995, 1996, 1997
Wai Ling Yee (Waterloo)	1999
Melanie E. Wood (Duke)	2001, 2002
Ana Caraiani (Princeton)	2003, 2004

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