Definitions

William Lowell Putnam Mathematical Competition

The William Lowell Putnam Mathematical Competition, often abbreviated to the Putnam Competition, is an annual mathematics competition for undergraduate college students of the United States and Canada, awarding scholarships and cash prizes ranging from \$250 to \$2,500 for the top students and \$5,000 to \$25,000 for the top schools. The competition was founded in 1927 by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam, 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.

Current Competition layout

The Putnam competition now takes place on the first Saturday in December, and consists of two three-hour sittings separated by a lunch break. Each competitor attempts to solve twelve problems, 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 10 points, and 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. In earlier years, the twelve questions were worth one point each, with absolutely no partial credit given. 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 there have been only three perfect scores as of 2005. In 2003, of the 3,615 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 compete; 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 an official team member. For example, in 2006, MIT had three of the top five scorers on the examination and nine of the top fifteen, while Princeton had just two students in the top fifteen; but Princeton took first place among teams while MIT took third.

The top five teams win \$25,000, \$20,000, \$15,000, \$10,000, and \$5,000, in that order, with team members receiving \$1,000, \$800, \$600, \$400, and \$200, respectively.

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 the American Mathematical Monthly.

The competition is held on the first Saturday in December, most recently December 1, 2007. The 2008 exam will be held on December 6.

Many contestants have gone on to become distinguished researchers in mathematics and other fields, including three Fields MedalistsMilnor, Mumford, and Quillen — and two Nobel Prize winners in Physics — Feynman and Wilson.

Winners

Top-scoring teams

YearFirstSecondThirdFourthFifth
1938 Toronto  UC Berkeley  Columbia
1939 Brooklyn College  MIT  Mississippi Woman's
1940 Toronto  Yale  Columbia
1941 Brooklyn College  UPenn  MIT
1942 Toronto  Yale  MIT  City College of NY
1946 Toronto  MIT  Brooklyn College  Carnegie Tech
1947 Harvard  Yale  Columbia  UPenn
1948 Brooklyn College  Toronto  Harvard City College of NY  and  McGill
1949 Harvard  Toronto  Carnegie Tech  City College of NY
1950 Caltech  Harvard  NYU  Toronto
1951 Cornell  Harvard  Cooper Union  City College of NY
1952 Queen's  Brooklyn Polytech  Harvard  MIT
1953 Harvard  City College of NY  Cornell  UC Berkeley
1954 Cornell  Harvard  MIT  Toronto
1955 Harvard  Toronto  Yale  Kenyon
1956 Harvard  Columbia  Queen's  MIT
1957 Harvard  Columbia  Cornell  Caltech
1958 (Spring) Brooklyn Polytech  Harvard  Toronto  Manitoba
1958 (Fall) Harvard  Toronto  Caltech  Cornell
1959 Brooklyn Polytech  Caltech  Toronto  Harvard  Case Tech
1960 UC Berkeley  Harvard  MIT  Michigan State  Cornell
1961 Michigan State  MIT  Caltech  Harvard  Dartmouth
1962 Caltech  Dartmouth  Harvard  Queen's  UCLA
1963 Michigan State  Brooklyn College  UPenn  Caltech  MIT
1964 Caltech  MIT  Harvard  Case Tech  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 Tech  Caltech
1971 Caltech  Chicago  Harvard  UC Davis  MIT
1972 Caltech  Oberlin  Harvard  Swarthmore  MIT
1973 Caltech  British Columbia  Chicago  Harvard  Princeton
1974 Waterloo  Chicago  Caltech  MIT  British Columbia
1975 Caltech  Chicago  MIT  Princeton  Harvard
1976 Caltech  Washington U in StL  Princeton Case Western Reserve  and  MIT
1977 Washington U in StL  UC Davis  Caltech  Princeton  MIT
1978 Case Western Reserve  Washington U in StL  Waterloo  Harvard  Caltech
1979 MIT  Caltech  Princeton  Stanford  Waterloo
1980 Washington U in StL  Harvard  Maryland  Chicago  UC Berkeley
1981 Washington U in StL  Princeton  Harvard  Stanford  Maryland
1982 Harvard  Waterloo  Caltech  Yale  Princeton
1983 Caltech  Washington U in StL  Waterloo  Princeton  Chicago
1984UC Davis  and  Washington U in StL Harvard  Princeton  Yale
1985 Harvard  Princeton  UC Berkeley  Rice  Waterloo
1986 Harvard  Washington U in StL  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 U in StL
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 U in StL  Caltech
1997 Harvard  Duke  Princeton  MIT  Washington U in StL
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
2005 Harvard  Princeton  Duke  MIT  Waterloo
2006 Princeton  Harvard  MIT  Toronto  Chicago
2007 Harvard  Princeton  MIT  Stanford  Duke

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.

The following table lists Teams finishing in Top Five (as of 2007 competition):

Top FiveTeam (s)
53 Harvard
38 MIT
28 Caltech
26 Princeton
18 Toronto
17 Waterloo
12 Duke
11 Chicago, Washington U in StL, Yale
9 UC Berkeley, Cornell
6 Stanford
5 Brooklyn College, City College of NY, Michigan State
4 Case Western Reserve (including former Case Tech), Columbia, Michigan, Rice
3 Brooklyn Polytech, UC Davis, Carnegie Mellon (including former Carnegie Tech), Queen's, UPenn
2 British Columbia, Dartmouth, Harvey Mudd, Maryland, UCLA
1 Cooper Union, Illinois Tech, Kansas, Kenyon, Manitoba, McGill, Miami University,
Mississippi Woman's, NYU, Oberlin College, Swarthmore

The following table lists teams that finished in the top five since 1990 (as of 2007 competition):

Top FiveTeam (s)
17 Harvard
12 Duke, MIT
11 Princeton
8 Waterloo
5 Caltech
4 Stanford, Toronto
3 Cornell, Washington U in StL
2 Chicago, UC Berkeley, Harvey Mudd, University of Michigan, Yale
1 Miami University

The following table lists Teams with First place finishes (as of 2007 competition):

First placeTeam (s)
26 Harvard
9 Caltech
5 MIT
4 Toronto,Washington U in StL
3 Brooklyn College, Duke, Michigan State
2 Brooklyn Polytech, Cornell, Waterloo
1 UC Berkeley, UC Davis, Case Western Reserve, Chicago, Princeton, Queen's

Putnam Fellows

Since the first competition, the top five (or six, in case of a tie) scorers on the examination have been named Putnam Fellows. Within the top five, Putnam Fellows are not ranked. Students are not allowed to participate in the Putnam Competition more than four times. For example, if a high school senior chooses to officially participate, he/she effectively chooses to forfeit one of his/her years of eligibility in college (see Gabriel D. Carroll). This makes it even more of a remarkable feat to become a Putnam Fellow four times. In the history of Competition, only seven students have been Putnam Fellows four times, with sixteen others winning the award three times. The following table lists these students:

NameTeamYears
Don Coppersmith  MIT  1968  1969  1970  1971
Arthur Rubin  Purdue, Caltech  1970  1971  1972  1973
Bjorn Poonen  Harvard  1985  1986  1987  1988
Ravi D. Vakil  Toronto  1988  1989  1990  1991
Gabriel D. Carroll  UC Berkeley, Harvard  2000  2001  2002  2003
Reid W. Barton  MIT  2001  2002  2003  2004
Daniel Kane  MIT  2003  2004  2005  2006
Edward L. Kaplan  Carnegie Tech  1939  1940  1941
Andrew M. Gleason  Yale  1940  1941  1942
Donald J. Newman  City College of NY  1948  1949  1950
James B. Herreshoff IV  UC Berkeley  1951  1952  1953
Samuel Jacob Klein  City College of NY  1953  1959  1960
Randall L. Dougherty  UC Berkeley  1978  1979  1980
Eric D. Carlson  Michigan State  1980  1982  1983
David W. Ash  Waterloo  1981  1982  1983
Noam D. Elkies  Columbia  1982  1983  1984
David J. Grabiner  Princeton  1986  1987  1988
David J. Moews  Harvard  1986  1987  1988
J. P. Grossman  Toronto  1993  1994  1995
Kiran S. Kedlaya  Harvard  1993  1994  1995
Lenhard L. Ng  Harvard  1993  1994  1995
Ciprian Manolescu  Harvard  1997  1998  2000
Aaron C. Pixton  Princeton  2004  2005  2007

The following table lists all Putnam fellows from 1938 to present, with the years they placed in the top five.

Name (Team)Year (s)
George W. Mackey (Rice)  1938
Irving Kaplansky (Toronto)  1938
Michael J. Norris (College of St. Thomas 1938
Robert W. Gibson (Fort Hays Kansas State 1938
Bernard Sherman (Brooklyn College)  1938, 1939
Abraham Hillman (Brooklyn College)  1939
Richard P. Feynman (MIT)  1939
William Nierenberg (City College of NY)  1939
Edward L. Kaplan (Carnegie Tech)  1939, 1940, 1941
John Cotton Maynard (Toronto)  1940
Robert Maughan Snow (George Washington 1940
W. J. R. Crosby (Toronto)  1940
Andrew M. Gleason (Yale)  1940, 1941, 1942
Paul C. Rosenbloom (UPenn)  1941
Richard F. Arens (UCLA)  1941
Harold Victor Lyons (Toronto)  1942
Harvey Cohn (City College of NY)  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 (UPenn)  1947
Eoin L. Whitney (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 NY)  1948, 1949, 1950
Ariel Zemach (Harvard)  1949
David L. Yarmush (Harvard)  1949
John W. Milnor (Princeton)  1949, 1950
John P. Mayberry (Toronto)  1950
Richard J. Semple (Toronto)  1950
Z. Alexander Melzak (British Columbia)  1950
Arthur P. Dempster (Toronto)  1951
Harold Widom (City College of NY)  1951
Herbert C. Kranzer (NYU)  1951
Peter John Redmond (Cooper Union)  1951
James B. Herreshoff IV (UC Berkeley)  1951, 1952, 1953
Eugene R. Rodemich (Washington U in StL)  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 NY)  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)  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)  Spring 1958
Lawrence A. Shepp (Brooklyn Polytech)  Spring 1958
Richard M. Dudley (Harvard)  Spring 1958
Joseph Lipman (Toronto)  Spring 1958, Fall 1958
Alan Gaisford Waterman (San Diego State Fall 1958
John Rex Forrester Hewett (Toronto)  Fall 1958
Robin C. Hartshorne (Harvard)  Fall 1958
Alfred W. Hales (Caltech)  Fall 1958, 1959
Daniel G. Quillen (Harvard)  1959
Donald Passman (Brooklyn Polytech)  1959
Donald S. Gorman (Harvard)  1959
Martin Isaacs (Brooklyn Polytech)  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 (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 (Robert) Bowen (UC Berkeley)  1964, 1965
Vern Poythress (Caltech)  1964
Andreas R. Blass (Detroit 1965
Barry Simon (Harvard)  1965
Daniel Fendel (Harvard)  1965
Lon M. Rosen (Toronto)  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, 1973
Dale Peterson (Yale)  1971
David Shucker (Swarthmore)  1971
Robert Israel (Chicago)  1971
Michael Yoder (Caltech)  1971, 1972
Arthur Rothstein (Reed 1972
David Vogan (Chicago)  1972
Dean Hickerson (UC Davis)  1972
Ira Gessel (Harvard)  1972
Angelos J. Tsirimokos (Princeton)  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
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 U in StL)  1976
Steven T. Tschantz (UC Berkeley)  1976, 1978
Michael Roberts (MIT)  1977
Paul A. Vojta (Minnesota)  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)  1979
Daniel J. Goldstein (Chicago)  1980
Laurence E. Penn (Harvard)  1980
Michael Raship (Harvard)  1980
Eric D. Carlson (Michigan State)  1980, 1982, 1983
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)  1982
Edward A. Shpiz (Washington U in StL)  1982
Noam D. Elkies (Columbia)  1982, 1983, 1984
Gregg N. Patruno (Princeton)  1983
Benji N. Fisher (Harvard)  1984
Daniel W. Johnson (Rose-Hulman Tech 1984
Richard A. Stong (Washington U in StL)  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 Poonen (Harvard)  1985, 1986, 1987, 1988
David I. 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
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
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 U in StL)  1996, 1997
Ovidiu Savin (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 NY 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, 2005, 2006
Aaron C. Pixton (Princeton)  2004, 2005, 2007
Oleg I. Golberg (MIT)  2005
Matthew M. Ince (MIT)  2005
Ricky I. Liu (Harvard)  2005
Tiankai Liu (Harvard)  2005, 2006
Hansheng Diao (MIT)  2006
Po-Ru Loh (Caltech)  2006
Yufei Zhao (MIT)  2006
Jason C. Bland (Caltech)  2007
Brian R. Lawrence (Caltech)  2007
Qingchun Ren (MIT)  2007
Xuancheng Shao (MIT)  2007
Arnav Tripathy (Harvard)  2007

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.  Names in bold have been Putnam Fellows at least once; the year(s) in which they were Fellows are in bold as well.

NameTeamYear (s)
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
Alison B. Miller  Harvard  2005, 2006, 2007

Trivia

A gift to the 2006 Putnam participants, a mug, had the first problem from that test printed on it. The problem was to find the volume of an object using only its equation. The object turned out to be a torus, and its being on the mug may be a reference to a donut (which is shaped like a torus) being indistinguishable from a coffee mug when considered by a topologist.