# 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 enrolled at institutions of higher learning in the United States and Canada (regardless of the students' nationalities). It awards a scholarship and cash prizes ranging from $250 to $2,500 for the top students and $5,000 to $25,000 for the top schools, plus one of the top five individual scorers (designated as *Putnam Fellows*) is awarded a scholarship of up to $12,000 plus tuition at Harvard University (Putnam Fellow Prize Fellowship),[1] the top 100 individual scorers have their names mentioned in the American Mathematical Monthly (alphabetically ordered within rank), and the names and addresses of the top 500 contestants are mailed to all participating institutions. It is widely considered to be the most prestigious university-level mathematics competition in the world, and its difficulty is such that the median score is often zero (out of 120) despite being attempted by students specializing in mathematics.[2][3]

The competition was founded in 1927 by Elizabeth Lowell Putnam in memory of her husband William Lowell Putnam, who was an advocate of intercollegiate intellectual competition. The exam has been offered annually since 1938 and is administered by the Mathematical Association of America.[4]

## 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. The test is supervised by faculty members at the participating schools. Each test consists of twelve challenging problems. The problems cover a range of advanced material in undergraduate mathematics, including concepts from group theory, set theory, graph theory, lattice theory, and number theory. [5]

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 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 zero or one point out of 120 possible, and there have been only four perfect scores as of 2010. 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 percentile.

At a participating college, any student who wishes to take part in the exam may compete (limited by the number of exams a school receives); but until 2019 the school's official team consisted of three individuals whom it designated in advance. Until 2019, a team's score was the sum of the ranks of its three team members, with the lowest cumulative rank winning. It was 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 2010, MIT had two of the top five scorers on the examination and seven of the top 24, while Caltech had just one student in the top five and only four in the top 24; yet Caltech took first place among teams while MIT took second.[6] In 2019 the rules of the competition changed, with a school's team consisting of its top three scorers, and team ranks determined by comparing the sums of the scores of the team members. [7]

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. The school with the first-place team receives an award of $25,000. Each first-place team member, as well as the winner of the Elizabeth Lowell Putnam Prize, receives $1,000. 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*, and exam results are published in early April of the year following the exam.[8]

Many Putnam Fellows have gone on to become distinguished researchers in mathematics and other fields, including three Fields Medalists—Milnor, Mumford, and Quillen—and two Nobel laureates in physics—Feynman and Wilson.

## Winners

### Top-scoring teams

Year | First | Second | Third | Fourth | Fifth |
---|---|---|---|---|---|

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 McGilland | |

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 MITand | |

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 |

1984 |
UC Davis Washington U in StLand |
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 |

2008 |
Harvard | Princeton | MIT | Stanford | Caltech |

2009 |
MIT | Harvard | Caltech | Stanford | Princeton |

2010 |
Caltech | MIT | Harvard | UC Berkeley | Waterloo |

2011 |
Harvard | Carnegie Mellon | Caltech | Stanford | MIT |

2012 |
Harvard | MIT | UCLA | Stony Brook | Carnegie Mellon |

2013 |
MIT | Carnegie Mellon | Stanford | Harvard | Caltech |

2014 |
MIT | Harvard | RPI | Waterloo | Carnegie Mellon |

2015 |
MIT | Carnegie Mellon | Princeton | Stanford | Harvard |

2016 |
Carnegie Mellon | Princeton | Harvard | MIT | Stanford |

2017 |
MIT | Harvard | Princeton | Toronto | UCLA |

2018 |
Harvard | MIT | UCLA | Columbia | Stanford |

### Teams ranked by historical performance

Below is a table of teams by the number of appearances in the top five and number of titles.

The following table lists Teams finishing in Top Five (as of 2018 competition):

Top Five | Team (s) |
---|---|

64 |
Harvard |

49 |
MIT |

33 |
Caltech |

31 |
Princeton |

19 |
Waterloo, Toronto |

13 |
Stanford |

12 |
Duke |

11 |
Chicago, Washington U in StL, Yale |

10 |
UC Berkeley, Cornell |

9 |
Carnegie Mellon (including former Carnegie Tech) |

6 |
Columbia |

5 |
Brooklyn College, City College of NY, Michigan State, UCLA |

4 |
Case Western Reserve (including former Case Tech), Michigan, Rice |

3 |
Brooklyn Polytech, UC Davis, Queen's, UPenn |

2 |
British Columbia, Dartmouth, Harvey Mudd, Maryland |

1 |
Cooper Union, Illinois Tech, Kansas, Kenyon, Manitoba, McGill, Miami University, RPI NYU, Oberlin College, SUNY Stony Brook, Swarthmore, William Carey (under former name of Mississippi Woman's) |

For a recent analysis, the following table lists teams that finished in the top five since 2000 (as of 2018 competition):

Top Five | Team (s) |
---|---|

18 |
Harvard, MIT |

10 |
Princeton, Stanford |

8 |
Caltech |

7 |
Duke |

6 |
Carnegie Mellon |

4 |
Waterloo |

3 |
UC Berkeley, Toronto, UCLA |

1 |
Chicago, Harvey Mudd, Stony Brook, RPI, Columbia |

The following table lists Teams with First place finishes (as of 2018 competition):

First Place | Team (s) |
---|---|

30 |
Harvard |

10 |
Caltech, MIT |

4 |
Toronto, Washington U in StL |

3 |
Brooklyn College, Duke, Michigan State |

2 |
Brooklyn Polytech, Cornell, Waterloo |

1 |
UC Berkeley, UC Davis, Carnegie Mellon, 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 Carroll). This makes it even more of a remarkable feat to become a Putnam Fellow four times. In the history of the Competition, only eight students have been Putnam Fellows four times, with twenty-three others winning the award three times. The following table lists these students:

Name | School | Years | |||
---|---|---|---|---|---|

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 |

Brian R. Lawrence | Caltech | 2007 | 2008 | 2010 | 2011 |

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 Pixton | Princeton | 2004 | 2005 | 2007 | |

Yufei Zhao | MIT | 2006 | 2008 | 2009 | |

Arnav Tripathy | Harvard | 2007 | 2008 | 2009 | |

Seok Hyeong Lee | Stanford | 2008 | 2010 | 2011 | |

Evan O'Dorney | UC Berkeley, Harvard | 2011 | 2012 | 2013 | |

Zipei Nie | MIT | 2012 | 2013 | 2014 | |

David Yang | MIT | 2013 | 2014 | 2015 | |

Yunkun Zhou | MIT | 2015 | 2016 | 2017 |

The following table lists all Putnam fellows from 1938 to present, with the years they placed in the top five.[9]

Name (School) | 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 |

Samuel I. Askovitz (UPenn) | 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 Lewis Baily, 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 |

I. Martin Isaacs (Brooklyn Polytech) | 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 (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 (UNC Chapel Hill) | 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 K. Winkler (MIT) | 1969, 1970 |

Robert A. Oliver (Chicago) | 1969, 1970 |

Jeffrey Lagarias (MIT) | 1970 |

Jockum Aniansson (Yale) | 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 |

Franklin T. Adams (Chicago) | 1975 |

Christopher L. Henley (Caltech) | 1975, 1976 |

David J. Wright (Cornell) | 1976 |

Nathaniel S. Kuhn (Harvard) | 1976 |

Paul M. Herdeg (Case Western Reserve) | 1976 |

Philip I. Harrington (Washington U in StL) | 1976 |

Steven T. Tschantz (UC Berkeley) | 1976, 1978 |

Adam L. Stephanides (Chicago) | 1977, 1981 |

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 |

Christos A. 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 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 U in StL) | 1996, 1997 |

Ovidiu Savin (Pittsburgh) | 1997 |

Patrick K. Corn (Harvard) | 1997 |

Samuel Grushevsky (Harvard) | 1997 |

Mike 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 |

Stewart Ellis (OSU) | 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 College 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 |

Vladimir V. Barzov (MIT) | 2004 |

Aaron Pixton (Princeton) | 2004, 2005, 2007 |

Oleg 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, 2008, 2009 |

Jason C. Bland (Caltech) | 2007 |

Brian R. Lawrence (Caltech) | 2007, 2008, 2010, 2011 |

Qingchun Ren (MIT) | 2007, 2009 |

Xuancheng Shao (MIT) | 2007 |

Arnav Tripathy (Harvard) | 2007, 2008, 2009 |

Seok Hyeong Lee (Stanford) | 2008, 2010, 2011 |

Bohua Zhan (MIT) | 2008 |

William Johnson (U of Washington) | 2009 |

Xiaosheng Mu (Yale) | 2009, 2011 |

Yu Deng (MIT) | 2010 |

Colin P. Sandon (MIT) | 2010 |

Alex (Lin) Zhai (Harvard) | 2010 |

Samuel S. Elder (Caltech) | 2011 |

Evan O'Dorney (Harvard) | 2011, 2012, 2013 |

Benjamin P. Gunby (MIT) | 2012 |

Eric K. Larson (Harvard) | 2012 |

Mitchell M. Lee (MIT) | 2012, 2013 |

Zipei Nie (MIT) | 2012, 2013, 2014 |

Bobby Shen (MIT) | 2013, 2014 |

David Yang (MIT) | 2013, 2014, 2015 |

Ravi Jagadeesan (Harvard) | 2014 |

Mark Sellke (MIT) | 2014 |

Lingfu Zhang (MIT) | 2014 |

Pakawut Jiradilok (Harvard) | 2015 |

Bumsoo Kim (Princeton) | 2015 |

Gyujin Oh (Stanford) | 2015 |

Daniel Spivak (Waterloo) | 2015 |

Yunkun Zhou (MIT) | 2015, 2016, 2017 |

Joshua D. Brakensiek (Carnegie Mellon) | 2016 |

Dong Ryul Kim (Harvard) | 2016, 2018 |

Thomas E. Swayze (Carnegie Mellon) | 2016 |

Samuel Zbarsky (Carnegie Mellon) | 2016 |

David Stoner (Harvard) | 2017, 2018 |

Ömer Cerrahoğlu (MIT) | 2017 |

Jiyang Gao (MIT) | 2017 |

Junyao Peng (MIT) | 2017 |

Ashwin Sah (MIT) | 2017 |

Yuan Yao (MIT) | 2018 |

Shengtong Zhang (MIT) | 2018 |

Shyam Narayanan (Harvard) | 2018 |

### 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. The year(s) in which they were Fellows are in **bold**.

Name | School | Year (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 |

Viktoriya Krakovna | Toronto | 2008 |

Yinghui Wang | MIT | 2010 |

Fei Song | Virginia | 2011 |

Xiao Wu | Yale | 2013 |

Simona Diaconu | Princeton | 2016 |

Ni Yan | UCLA | 2017 |

Danielle Wang | MIT | 2015, 2018 |

## References

- "William Lowell Putnam Competition Prizes".
*math.scu.edu*. Santa Clara University. - "Putnam Competition | Mathematical Association of America".
*www.maa.org*. Retrieved 18 April 2018. - David Arney; George Rosenstein. "The Harvard-United States Military Academy Mathematics Competition of 1933: Genesis of the William Lowell Putnam Mathematical Competition".
*www.westpoint.edu*. Retrieved 18 April 2018. - "History of the Putnam Prize".
*Santa Clara University – Mathematics & Computer Science*. Retrieved 18 April 2018. - https://www.maa.org/math-competitions/putnam-competition
- Fujimori, Jessica (3 May 2016). "At Putnam, students rise to the challenge".
*news.mit.edu*. MIT News. Retrieved 18 April 2018. - https://www.maa.org/math-competitions/putnam-competition
- Weisstein, Eric (17 April 2018). "Putnam Mathematical Competition".
*mathworld.wolfram.com*. Wolfram Web Resources. Retrieved 18 April 2018. - Gallian, Joseph A. (October 2004). "The First Sixty-Six Years of the Putnam Competition".
*The American Mathematical Monthly*.**111**(8): 691–699. doi:10.2307/4145042. JSTOR 4145042.(registration required)

## External links

Wikimedia Commons has media related to .Putnam Fellows |

- William Lowell Putnam Mathematical Competition results
- William Lowell Putnam Competition problems, solutions, and results archive
- Archive of Problems 1938–2003
- Searchable data base for information about careers of Putnam Fellows
- A comprehensive history of the Putnam competition An electronic update of Gallian's 2004 paper (PDF)