The William Lowell Putnam Mathematical Competition, often truncated to Putnam Competition, is an annual mathematics competition for undergraduate college students enrolled at institutions of higher learning in the United States, Canada, and Mexico (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 (designated as Putnam Fellows) is awarded a scholarship of up to $12,000 plus tuition at Harvard University (Putnam Fellow Prize Fellowship), 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 or one (out of 120) despite being primarily 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 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 five perfect scores . In 2003, of the 3,615 students competing, 1,024 (28%) scored 10 or more points, and 42 points was sufficient to make the top percentile. In 2024, 3,988 students competed with 1,273 (32%) scoring 10 or more points with 48 points were needed to rank 100.
At a participating college, any student who wishes to take part in the competition may (limited by the number of spots 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 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.
Awards 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—John Milnor (also an Abel Prize laureate), David Mumford, and Daniel Quillen—and two Nobel laureates in physics—Richard Feynman and Kenneth 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 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 1984 UC 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 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 2019 MIT Harvard Stanford UCLA Waterloo 2021 MIT Princeton Harvard Stanford UCLA 2022 MIT Harvard Stanford Maryland Yale 2023 MIT Harvard Duke Stanford Toronto 2024 MIT Harvard Stanford Carnegie Mellon UC Santa Barbara 2025 MIT Chicago Harvard Stanford 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.
The following table lists Teams finishing in Top Five ( competition): Top Five Team(s) 70 Harvard 55 MIT 34 Caltech 33 Princeton 20 Toronto, Waterloo 19 Stanford 12 Yale, Duke, Chicago 11 Washington University in St. Louis 10 UC Berkeley, Cornell, Carnegie Mellon (including former Carnegie Tech) 7 UCLA 6 Columbia 5 Brooklyn College, City College of New York, Michigan State 4 Case Western Reserve (including former Case Tech), Michigan, Rice 3 Brooklyn Polytech, UC Davis, Queen's, Penn, Maryland 2 British Columbia, Dartmouth, Harvey Mudd 1 UC Santa Barbara, Cooper Union, Illinois Tech, Kansas, Kenyon, Manitoba, McGill, Miami University, RPI NYU, Oberlin, 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 ( competition): Top Five Team(s) 24 Harvard, MIT 16 Stanford 11 Princeton 9 Caltech 8 Duke 7 Carnegie Mellon 5 UCLA, Waterloo 4 Toronto 3 UC Berkeley 2 Chicago 1 UC Santa Barbara, Harvey Mudd, Stony Brook, Yale, RPI, Columbia, Maryland
The following table lists Teams with First place finishes ( competition): First Place Team(s) 30 Harvard 16 MIT 10 Caltech 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 (or six, in case of a tie) 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 (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 nine students have been Putnam Fellows four times, with twenty-four others winning the award three times. The following table lists these students: