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. 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 is awarded a scholarship of up to $12,000 plus tuition at Harvard University, the top 100 individual scorers have their names mentioned in the American Mathematical Monthly, 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 despite being attempted by students specializing in mathematics.
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 competition has been offered annually since 1938 and is administered by the Mathematical Association of America.
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 competition is supervised by faculty members at the participating schools. Each one 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.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 competition 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. In 2003, of the 3,615 students competing, 1,024 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 competition may ; 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 in the competition 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. 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.
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 competition results are published in early April of the year following the competition.
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
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 :
| Top Five | Team |
| 65 | Harvard |
| 50 | MIT |
| 33 | Caltech |
| 31 | Princeton |
| 20 | Waterloo |
| 19 | Toronto |
| 14 | Stanford |
| 12 | Duke |
| 11 | Chicago, Washington University in St. Louis, Yale |
| 10 | UC Berkeley, Cornell |
| 9 | Carnegie Mellon |
| 6 | Columbia, UCLA |
| 5 | Brooklyn College, City College of New York, Michigan State |
| 4 | Case Western Reserve, Michigan, Rice |
| 3 | Brooklyn Polytech, UC Davis, Queen's, Penn |
| 2 | British Columbia, Dartmouth, Harvey Mudd, Maryland |
| 1 | Cooper Union, Illinois Tech, Kansas, Kenyon, Manitoba, McGill, Miami University, RPI NYU, Oberlin, Stony Brook, Swarthmore, William Carey |
For a recent analysis, the following table lists teams that finished in the top five since 2000 :
| Top Five | Team |
| 19 | Harvard, MIT |
| 11 | Stanford |
| 10 | Princeton |
| 8 | Caltech |
| 7 | Duke |
| 6 | Carnegie Mellon |
| 5 | Waterloo |
| 4 | UCLA |
| 3 | UC Berkeley, Toronto |
| 1 | Chicago, Harvey Mudd, Stony Brook, RPI, Columbia |
The following table lists Teams with First place finishes :
| First Place | Team |
| 30 | Harvard |
| 10 | Caltech, MIT |
| 4 | Toronto, Washington University in St. Louis |
| 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 scorers in the competition 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. 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:The following table lists all Putnam fellows from 1938 to present, with the years they placed in the top five.
| Name | Year |
| George W. Mackey | 1938 |
| Irving Kaplansky | 1938 |
| Michael J. Norris | 1938 |
| Robert W. Gibson | 1938 |
| Bernard Sherman | 1938, 1939 |
| Abraham Hillman | 1939 |
| Richard P. Feynman | 1939 |
| William Nierenberg | 1939 |
| Edward L. Kaplan | 1939, 1940, 1941 |
| John Cotton Maynard | 1940 |
| Robert Maughan Snow | 1940 |
| W. J. R. Crosby | 1940 |
| Andrew M. Gleason | 1940, 1941, 1942 |
| Paul C. Rosenbloom | 1941 |
| Richard F. Arens | 1941 |
| Samuel I. Askovitz | 1941 |
| Harold Victor Lyons | 1942 |
| Harvey Cohn | 1942 |
| Melvin A. Preston | 1942 |
| Warren S. Loud | 1942 |
| Donald A. Fraser | 1946 |
| Eugenio Calabi | 1946 |
| Felix Browder | 1946 |
| J. Arthur Greenwood | 1946 |
| Maxwell A. Rosenlicht | 1946, 1947 |
| Clarence Wilson Hewlett, Jr. | 1947 |
| William Turanski | 1947 |
| Eoin L. Whitney | 1947, 1948 |
| W. Forrest Stinespring | 1947, 1949 |
| George F. D. Duff | 1948 |
| Harry Gonshor | 1948 |
| Leonard Geller | 1948 |
| Robert L. Mills | 1948 |
| Donald J. Newman | 1948, 1949, 1950 |
| Ariel Zemach | 1949 |
| David L. Yarmush | 1949 |
| John W. Milnor | 1949, 1950 |
| John P. Mayberry | 1950 |
| Richard J. Semple | 1950 |
| Z. Alexander Melzak | 1950 |
| Arthur P. Dempster | 1951 |
| Harold Widom | 1951 |
| Herbert C. Kranzer | 1951 |
| Peter John Redmond | 1951 |
| James B. Herreshoff IV | 1951, 1952, 1953 |
| Eugene R. Rodemich | 1952 |
| Gerhard Rayna | 1952 |
| Richard G. Swan | 1952 |
| Walter Lewis Baily, Jr. | 1952 |
| Marshall L. Freimer | 1953 |
| Norman Bauman | 1953 |
| Tai Tsun Wu | 1953 |
| Samuel Jacob Klein | 1953, 1959, 1960 |
| Benjamin Muckenhoupt | 1954 |
| James Daniel Bjorken | 1954 |
| Leonard Evens | 1954 |
| William P. Hanf | 1954 |
| Kenneth G. Wilson | 1954, 1956 |
| Howard C. Rumsey, Jr. | 1955 |
| Jack Towber | 1955 |
| David B. Mumford | 1955, 1956 |
| Trevor Barker | 1955, 1956 |
| Everett C. Dade | 1955, 1957 |
| Richard Michael Friedberg | 1956 |
| David M. Bloom | 1956, 1957 |
| J. Ian Richards | 1957 |
| Richard T. Bumby | 1957 |
| Rohit J. Parikh | 1957 |
| David R. Brillinger | Spring 1958 |
| Donald J. C. Bures | Spring 1958 |
| Lawrence A. Shepp | Spring 1958 |
| Richard M. Dudley | Spring 1958 |
| Joseph Lipman | Spring 1958, Fall 1958 |
| Alan Gaisford Waterman | Fall 1958 |
| John Rex Forrester Hewett | Fall 1958 |
| Robin C. Hartshorne | Fall 1958 |
| Alfred W. Hales | Fall 1958, 1959 |
| Daniel G. Quillen | 1959 |
| Donald Passman | 1959 |
| Donald S. Gorman | 1959 |
| I. Martin Isaacs | 1959 |
| Stephen L. Adler | 1959 |
| Stephen Lichtenbaum | 1959 |
| Jon H. Folkman | 1960 |
| Louis Jaeckel | 1960 |
| Melvin Hochster | 1960 |
| William R. Emerson | 1960 |
| Barry Wolk | 1961 |
| Elwyn R. Berlekamp | 1961 |
| Edward Anton Bender | 1961, 1962 |
| John Hathaway Lindsey | 1961, 1962 |
| William C. Waterhouse | 1961, 1962 |
| John William Wood | 1962 |
| Robert S. Strichartz | 1962 |
| Joel H. Spencer | 1963 |
| Lawrence A. Zalcman | 1963 |
| Lawrence J. Corwin | 1963 |
| Robert E. Greene | 1963 |
| Stephen E. Crick, Jr. | 1963 |
| Barry B. MacKichan | 1964 |
| Fred William Roush | 1964 |
| Roger E. Howe | 1964 |
| Rufus Bowen | 1964, 1965 |
| Vern Poythress | 1964 |
| Andreas R. Blass | 1965 |
| Barry Simon | 1965 |
| Daniel Fendel | 1965 |
| Lon M. Rosen | 1965 |
| Marshall W. Buck | 1966 |
| Robert E. Maas | 1966 |
| Robert S. Winternitz | 1966 |
| Theodore C. Chang | 1966 |
| Richard C. Schroeppel | 1966, 1967 |
| David R. Haynor | 1967 |
| Dennis A. Hejhal | 1967 |
| Don B. Zagier | 1967 |
| Peter L. Montgomery | 1967 |
| Dean G. Huffman | 1968 |
| Gerald S. Gras | 1968 |
| Neal Koblitz | 1968 |
| Gerald A. Edgar | 1968, 1969 |
| Don Coppersmith | 1968, 1969, 1970, 1971 |
| Alan R. Beale | 1969 |
| Steven K. Winkler | 1969, 1970 |
| Robert A. Oliver | 1969, 1970 |
| Jeffrey Lagarias | 1970 |
| Jockum Aniansson | 1970 |
| Arthur Rubin | 1970, 1971, 1972, 1973 |
| Dale Peterson | 1971 |
| David Shucker | 1971 |
| Robert Israel | 1971 |
| Michael Yoder | 1971, 1972 |
| Arthur Rothstein | 1972 |
| David Vogan | 1972 |
| Dean Hickerson | 1972 |
| Ira Gessel | 1972 |
| Angelos J. Tsirimokos | 1973 |
| Matthew L. Ginsberg | 1973 |
| Peter G. De Buda | 1973 |
| David J. Anick | 1973, 1975 |
| Grant M. Roberts | 1974 |
| James B. Saxe | 1974 |
| Karl C. Rubin | 1974 |
| Philip N. Strenski | 1974 |
| Thomas G. Goodwillie | 1974, 1975 |
| Ernest S. Davis | 1975 |
| Franklin T. Adams | 1975 |
| Christopher L. Henley | 1975, 1976 |
| David J. Wright | 1976 |
| Nathaniel S. Kuhn | 1976 |
| Paul M. Herdeg | 1976 |
| Philip I. Harrington | 1976 |
| Steven T. Tschantz | 1976, 1978 |
| Adam L. Stephanides | 1977, 1981 |
| Michael Roberts | 1977 |
| Paul A. Vojta | 1977 |
| Stephen W. Modzelewski | 1977 |
| Russell D. Lyons | 1977, 1978 |
| Mark R. Kleiman | 1978 |
| Peter W. Shor | 1978 |
| Randall L. Dougherty | 1978, 1979, 1980 |
| Charles H. Walter | 1979 |
| Mark G. Pleszkoch | 1979 |
| Miller Puckette | 1979 |
| Richard Mifflin | 1979 |
| Daniel J. Goldstein | 1980 |
| Laurence E. Penn | 1980 |
| Michael Raship | 1980 |
| Eric D. Carlson | 1980, 1982, 1983 |
| Robin A. Pemantle | 1981 |
| Scott R. Fluhrer | 1981 |
| David W. Ash | 1981, 1982, 1983 |
| Michael J. Larsen | 1981, 1983 |
| Brian R. Hunt | 1982 |
| Edward A. Shpiz | 1982 |
| Noam D. Elkies | 1982, 1983, 1984 |
| Gregg N. Patruno | 1983 |
| Benji N. Fisher | 1984 |
| Daniel W. Johnson | 1984 |
| Richard A. Stong | 1984 |
| Michael Reid | 1984, 1987 |
| Everett W. Howe | 1985 |
| Keith A. Ramsay | 1985 |
| Martin V. Hildebrand | 1985 |
| Douglas S. Jungreis | 1985, 1986 |
| Bjorn Poonen | 1985, 1986, 1987, 1988 |
| David I. Zuckerman | 1986 |
| Waldemar P. Horwat | 1986 |
| David J. Grabiner | 1986, 1987, 1988 |
| David J. Moews | 1986, 1987, 1988 |
| Constantin S. Teleman | 1987 |
| John S. Tillinghast | 1987 |
| Jeremy A. Kahn | 1988 |
| Ravi D. Vakil | 1988, 1989, 1990, 1991 |
| Andrew H. Kresch | 1989 |
| Christos A. Athanasiadis | 1989 |
| Colin M. Springer | 1989 |
| Sihao Wu | 1989 |
| William P. Cross | 1989 |
| Jordan Lampe | 1990 |
| Raymond M. Sidney | 1990 |
| Eric K. Wepsic | 1990, 1991 |
| Jordan S. Ellenberg | 1990, 1992 |
| Joshua B. Fischman | 1991 |
| Xi Chen | 1991 |
| Samuel A. Kutin | 1991, 1992 |
| Jeffrey M. Vanderkam | 1992 |
| Serban M. Nacu | 1992 |
| Adam Logan | 1992, 1993 |
| Craig B. Gentry | 1993 |
| Wei-Hwa Huang | 1993 |
| J. P. Grossman | 1993, 1994, 1995 |
| Kiran S. Kedlaya | 1993, 1994, 1995 |
| Lenhard L. Ng | 1993, 1994, 1995 |
| William R. Mann | 1994 |
| Jeremy L. Bem | 1994, 1996 |
| Sergey V. Levin | 1995 |
| Yevgeniy Dodis | 1995 |
| Dragos N. Oprea | 1996 |
| Ioana Dumitriu | 1996 |
| Robert D. Kleinberg | 1996 |
| Stephen S. Wang | 1996 |
| Daniel K. Schepler | 1996, 1997 |
| Ovidiu Savin | 1997 |
| Patrick K. Corn | 1997 |
| Samuel Grushevsky | 1997 |
| Mike Develin | 1997, 1998 |
| Ciprian Manolescu | 1997, 1998, 2000 |
| Ari M. Turner | 1998 |
| Nathan G. Curtis | 1998 |
| Kevin D. Lacker | 1998, 2001 |
| Christopher C. Mihelich | 1999 |
| Colin A. Percival | 1999 |
| Davesh Maulik | 1999 |
| Derek I.E. Kisman | 1999 |
| Sabin Cautis | 1999 |
| Stewart Ellis | 1999 |
| Abhinav Kumar | 1999, 2000 |
| Pavlo Pylyavskyy | 2000 |
| Alexander B. Schwartz | 2000, 2002 |
| Gabriel D. Carroll | 2000, 2001, 2002, 2003 |
| George Lee, Jr. | 2001 |
| Jan K. Siwanowicz | 2001 |
| Reid W. Barton | 2001, 2002, 2003, 2004 |
| Deniss Cebikins | 2002 |
| Melanie E. Wood | 2002 |
| Ralph C. Furmaniak | 2003 |
| Ana Caraiani | 2003, 2004 |
| Daniel M. Kane | 2003, 2004, 2005, 2006 |
| Vladimir V. Barzov | 2004 |
| Aaron Pixton | 2004, 2005, 2007 |
| Oleg Golberg | 2005 |
| Matthew M. Ince | 2005 |
| Ricky I. Liu | 2005 |
| Tiankai Liu | 2005, 2006 |
| Hansheng Diao | 2006 |
| Po-Ru Loh | 2006 |
| Yufei Zhao | 2006, 2008, 2009 |
| Jason C. Bland | 2007 |
| Brian R. Lawrence | 2007, 2008, 2010, 2011 |
| Qingchun Ren | 2007, 2009 |
| Xuancheng Shao | 2007 |
| Arnav Tripathy | 2007, 2008, 2009 |
| Seok Hyeong Lee | 2008, 2010, 2011 |
| Bohua Zhan | 2008 |
| William Johnson | 2009 |
| Xiaosheng Mu | 2009, 2011 |
| Yu Deng | 2010 |
| Colin P. Sandon | 2010 |
| Alex Zhai | 2010 |
| Samuel S. Elder | 2011 |
| Evan O'Dorney | 2011, 2012, 2013 |
| Benjamin P. Gunby | 2012 |
| Eric K. Larson | 2012 |
| Mitchell M. Lee | 2012, 2013 |
| Zipei Nie | 2012, 2013, 2014 |
| Bobby Shen | 2013, 2014 |
| David Yang | 2013, 2014, 2015 |
| Ravi Jagadeesan | 2014 |
| Mark Sellke | 2014 |
| Lingfu Zhang | 2014 |
| Pakawut Jiradilok | 2015 |
| Bumsoo Kim | 2015 |
| Gyujin Oh | 2015 |
| Daniel Spivak | 2015 |
| Yunkun Zhou | 2015, 2016, 2017 |
| Joshua D. Brakensiek | 2016 |
| Dong Ryul Kim | 2016, 2018 |
| Thomas E. Swayze | 2016 |
| Samuel Zbarsky | 2016 |
| David Stoner | 2017, 2018 |
| Ömer Cerrahoğlu | 2017 |
| Jiyang Gao | 2017 |
| Junyao Peng | 2017 |
| Ashwin Sah | 2017, 2019 |
| Yuan Yao | 2018, 2019 |
| Shengtong Zhang | 2018, 2019 |
| Shyam Narayanan | 2018 |
| Kevin Sun | 2019 |
| Daniel Zhu | 2019 |
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, with three awards being made for the first time in 2019. The year in which they were Fellows are in bold.| Name | School | 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 |
| 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 |
| Laura Pierson | Harvard | 2019 |
| Qi Qi | MIT | 2019 |
| Hanzhi Zheng | Stanford | 2019 |