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威廉·洛厄爾·普特南數學競賽
来自维基百科，自由的百科全书
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威廉·洛厄爾·普特南數學競賽，通常簡稱為普特南競賽，是美國和加拿大高等教育機構註冊的本科大學生的年度數學競賽（沒有國籍限制）。它為頂尖學生頒發獎學金和現金獎勵，從 250 美元到 2,500 美元不等，為頂尖學校頒發 5,000 美元到 25,000 美元，此外，考試成績的前五名（被指定為普特南會員），在哈佛獲得最高12,000美元的獎學金（Putnam Fellow Prize Fellowship），[1]得分前100名的個人選手名字會被刊登在美國數學月刊（按字母順序排列），前500名選手的姓名和地址會被發送給所有參與機構。它以世界上最負盛名的大學生數學競賽被廣泛認可，其難度從儘管有數學系學生參與其中然中位數仍常常為零可見一斑（滿分120分）。
該競賽於1927年開始，由伊利沙伯·洛厄爾·普特南為紀念她的丈夫威廉·洛厄爾·普特南(William Lowell Putnam)設立。考試自1938年以來以每年一次的頻率進行（特例為1943、1944、1945停辦，1958年兩次），管理方為美國數學協會。
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比賽方式
普特南比賽通常在12月的第一個星期六舉行, 由兩次3個小時的考試組成, 由午休時間分開，一般學校會提供免費午餐。考試由參與學校的教職員工監督。這些問題通常需具備大學數學的基礎知識才能解決, 但需要廣泛的創造性思維。
12個問題中的每一題都值10分, 零以上的最常見分數是10分（完整答案/證明）, 9分（幾乎完整的答案/證明）, 以及1分（答案的最開始一部分，一般較為容易）。在前幾年, 這12個問題各值1分, 沒有給予部分得分。考試被普遍認為是極度困難的，通常只有專門學習數學的學生才能看懂並嘗試。 但中位分數通常是零或一分, 截至2010年, 只有4個滿分。2003年, 在3615名參加考試的學生中, 1024名考生(28%) 得了10分或10分以上, 若可以取得42分便足以達到最高的百分位（>=99%）。
在參與的學院（大學）, 任何希望參加考試的學生都可以參加考試 (受學校考試次數的限制); 在2019年之前，學校的隊伍由三名事先指定的個人組成。到2019年為止，每支隊伍的得分是3名隊員的排名之和，累積排名最低的隊伍獲勝。最終的結果完全有可能（甚至是在一些機構中常見的結果），表明選擇了 "錯誤" 的團隊--即一些不在官方團隊中的學生的得分超過了正式團隊成員。例如, 在 2010年, 麻省理工學院在考試前5名的得分手中有兩名, 在24強中有 7名, 而加州理工在前五名中只有一名學生, 在前24名中只有4名學生;但加州理工排名第一, 而麻省理工則位居第二。
按照這個順序, 前五名的團隊會依次贏得25,000美金、2,0000美金、15,000美金、15,000美金、10,000美金和5,000美元, 團隊成員會分別獲得1000美金，800美金，600美金，400美金和200美金。
前五名的個人得分手名叫普特南會員, 獎金為 2,500 美元。第一名的隊伍的學校獲得25000美金的獎勵。排名第一的隊伍的隊員以及伊利沙伯·洛厄爾·普特南獎的獲得者, 都能獲得 1,000 美元。第六至第15名的人可獲得 1,000 美元, 接下來的10人可獲得250美元。前100名學生的名字發表在《美國數學月刊》上, 考試成績在考試結束後的4月初公布。
許多普特南會員已成為數學和其他領域的傑出研究人員, 其中包括三名菲爾茲獎得主--米爾諾（同時也是阿貝爾獎的獲得主）、蒙福德和奎倫--以及兩位諾貝爾物理學獎獲得者--理查德·費曼和威爾遜。
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得獎者
更多資訊 年份, 第一名 ...
| 年份 | 第一名 | 第二名 | 第三名 | 第四名 | 第五名 |
|---|---|---|---|---|---|
| 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 和 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 和 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 和 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 |
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下面是按前五名的出場次數和冠軍數量列出的團隊表。
下表列出了在前五名 (截至2021年的比賽) 中完成的團隊:
更多資訊 前五名, 團隊 ...
| 前五名 | 團隊 |
|---|---|
| 68 | Harvard |
| 51 | MIT |
| 33 | Caltech |
| 32 | Princeton |
| 20 | Waterloo |
| 19 | Toronto |
| 15 | Stanford |
| 12 | Duke |
| 11 | Chicago, Washington University in St. Louis, Yale |
| 10 | UC Berkeley, Cornell |
| 9 | Carnegie Mellon(包括前身Carnegie Tech) |
| 7 | UCLA |
| 6 | Columbia |
| 5 | Brooklyn College, City College of New York, Michigan State |
| 4 | Case Western Reserve (包括前身Case Tech), Michigan, Rice |
| 3 | Brooklyn Polytech, UC Davis, Queen's University at Kingston, University of Pennsylvania |
| 2 | British Columbia, Dartmouth, Harvey Mudd, Maryland |
| 1 | Cooper Union, Illinois Tech, Kansas, Kenyon, Manitoba, McGill, Miami University, Rensselaer Polytechnic Institute,
NYU, Oberlin college, Stony Brook, Swarthmore college, William Carey (舊名為Mississippi Woman's) |
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下表列出了自 2000年 (截至2021年的比賽) 以來進入前五名的團隊:
更多資訊 前五名, 團隊 ...
| 前五名 | 團隊 |
|---|---|
| 20 | Harvard, MIT |
| 12 | Stanford |
| 11 | Princeton |
| 8 | Caltech |
| 7 | Duke |
| 6 | Carnegie Mellon |
| 5 | waterloo, UCLA |
| 3 | UC Berkeley, Toronto |
| 1 | Chicago, Harvey Mudd, Stony Brook, Rensselaer Polytechnic Institute , Columbia |
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下表列出了排名第一的團隊 (截至2021年的比賽):
更多資訊 第一名, 團隊 ...
| 第一名 | 團隊 |
|---|---|
| 30 | Harvard |
| 11 | MIT |
| 10 | Caltech |
| 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 |
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自第一場比賽以來, 考試成績最高的5人 (或6名, 如果打成平局) 被評為普特南會員。在前五名中, 普特南會員沒有排名。學生不得參加普特南比賽4次以上。例如, 如果一個高三學生選擇正式參與, 她實際上選擇放棄他在大學的幾年資格之一 (見加布里埃爾·卡羅爾)。這使得四次成為普特南會員更加了不起。在比賽歷史上, 只有8名學生曾4次擔任普特南會員, 另有23人三次獲獎。下表列出了這些學生:
更多資訊 名字, 學校 ...
| 名字 | 學校 | 年份 | |||
|---|---|---|---|---|---|
| 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 | |
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在下表中列出了1938年至今的所有普特南會員, 以及他們進入前五名的年份。
更多資訊 名字（學校）, 年份 ...
| 名字（學校） | 年份 |
|---|---|
| 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 |
| Thomas E. Swayze (Carnegie Mellon) | 2016 |
| Samuel Zbarsky (Carnegie Mellon) | 2016 |
| Ömer Cerrahoğlu (MIT) | 2017 |
| Jiyang Gao (MIT) | 2017 |
| Junyao Peng (MIT) | 2017 |
| Ashwin Sah (MIT) | 2017 |
| David Stoner (Harvard) | 2017 |
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