- 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 student s of theUnited States andCanada , awardingscholarship s 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 in1927 byElizabeth Lowell Putnam in memory of her husbandWilliam Lowell Putnam , who, while alive, was an advocate of intercollegiate intellectual competition. The exam has been offered annually since1938 and is administered by theMathematical 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 scoresas of 2005 . In2003 , 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 atHarvard 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 Medal ists —Milnor , Mumford, andQuillen — and twoNobel Prize winners 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 "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 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 Five Team (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 State4 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 , SwarthmoreThe following table lists teams that finished in the top five since 1990 (
as of 2007 competition):Top Five Team (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 , Yale1 Miami University The following table lists Teams with First place finishes (
as of 2007 competition):First place Team (s) 26 Harvard 9 Caltech 5 MIT 4 Toronto,Washington U in StL 3 Brooklyn College , Duke, Michigan State2 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:Name Team "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 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 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 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 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 (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 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 U in StL) 1976 Steven T. Tschantz (UC Berkeley) 1976, 1978 Adam L. Stephanides (Chicago) 1977 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 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) 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 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 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 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 Vladimir V. Barzov (MIT) 2004 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.
Name Team "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 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 atorus , 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.External links
* [http://math.scu.edu/putnam/index.html William Lowell Putnam Mathematical Competition official site]
* [http://www.maa.org/awards/putnam.html William Lowell Putnam Mathematical Competition results]
* [http://www.unl.edu/amc/a-activities/a7-problems/putnamindex.shtml William Lowell Putnam Competition problems, solutions, and results archive]
* [http://www.artofproblemsolving.com/Forum/index.php?f=80 Archive of Putnam Problems and Student Solutions]
* [http://www.dean.usma.edu/math/about/history/mathcomp.htm The Harvard-United States Military Academy Mathematics Competition of 1933: Genesis of the William Lowell Putnam Mathematical Competition]
* [http://www.d.umn.edu/~jgallian/putnamfel/PF.html Searchable data base for information about careers of Putnam Fellows]
* [http://www.d.umn.edu/~jgallian/putnam06.pdf A comprehensive history of the Putnam competition. ]
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