TheFrank Nelson Cole Prize, orCole Prize for short, is one of twenty-twoprizes awarded tomathematicians by theAmerican Mathematical Society, one for an outstanding contribution toalgebra, and the other for an outstanding contribution tonumber theory.[1] The prize is named afterFrank Nelson Cole, who served the Society for 25 years. The Cole Prize in algebra was funded by Cole himself, from funds given to him as a retirement gift; the prize fund was later augmented by his son, leading to the double award.[1][2]
The prizes recognize a notable research work in algebra (given every three years) or number theory (given every three years) that has appeared in the last six years. The work must be published in a recognized, peer-reviewed venue. The first award for algebra was made in 1928 toL. E. Dickson, while the first award for number theory was made in 1931 toH. S. Vandiver.[2]
| Year | Prizewinner | Citation |
|---|---|---|
| 1928 | Leonard E. Dickson | for his book "Algebren und ihre Zahlentheorie" |
| 1939 | Abraham Adrian Albert | for his papers on the construction ofRiemann matrices |
| 1944 | Oscar Zariski | for four papers onalgebraic varieties |
| 1949 | Richard Brauer | for his paper "On Artin'sL-series with general group characters" |
| 1954 | Harish-Chandra | for his papers on representations of semisimpleLie algebras andgroups |
| 1960 | Serge Lang | for his paper "Unramified classfield theory overfunction fields in several variables" |
| Maxwell A. Rosenlicht | for his papers "Generalized Jacobian varieties" and "A universal mapping property of generalized Jacobians" | |
| 1965 | Walter Feit John G. Thompson | for their joint paper "Solvability of groups of odd order" |
| 1970 | John R. Stallings | for his paper "Ontorsion-freegroups with infinitely many ends" |
| Richard G. Swan | for his paper "Groups ofcohomological dimension one" | |
| 1975 | Hyman Bass | for his paper "Unitaryalgebraic K-theory" |
| Daniel G. Quillen | for his paper "Higheralgebraic K-theories" | |
| 1980 | Michael Aschbacher | for his paper "A characterization ofChevalley groups overfields of odd order" |
| Melvin Hochster | for his paper "Topics in thehomological theory ofcommutative rings" | |
| 1985 | George Lusztig | for his fundamental work on therepresentation theory offinite groups ofLie type |
| 1990 | Shigefumi Mori | for his outstanding work on the classification ofalgebraic varieties |
| 1995 | Michel Raynaud David Harbater | for their solution ofAbhyankar's conjecture |
| 2000 | Andrei Suslin | for his work onmotivic cohomology |
| Aise Johan de Jong | for his important work on the resolution ofsingularities by genericallyfinite maps | |
| 2003 | Hiraku Nakajima | for his work inrepresentation theory andgeometry |
| 2006 | János Kollár | for his outstanding achievements in the theory ofrationally connected varieties and for his illuminating work on aconjecture of Nash |
| 2009 | Christopher Hacon James McKernan | for their groundbreaking joint work on higher dimensionalbirationalalgebraic geometry |
| 2012 | Alexander Merkurjev | for his work on theessential dimension ofgroups |
| 2015 | Peter Scholze | for his work onperfectoid spaces which has led to a solution of an important special case of theweight-monodromy conjecture ofDeligne |
| 2018 | Robert Guralnick | for his groundbreaking research on representation theory, cohomology, and subgroup structure of finite quasi-simple groups, and the wide-ranging applications of this work to other areas of mathematics. |
| 2021 | Chenyang Xu | for leading a group developing an algebraic theory of moduli for K-stable Fano varieties and working out a radically new approach to the singularities of the minimal model program using K-stability. |
| 2024 | Jessica Fintzen | for her work transforming the understanding of representations of p-adic groups, in particular for the article “Types for tame p-adic groups”. |
| Year | Prizewinner | Citation |
|---|---|---|
| 1931 | Harry Vandiver | for his several papers onFermat's last theorem |
| 1941 | Claude Chevalley | for his paper "La théorie du corps de classes" |
| 1946 | Henry B. Mann | for his paper "A proof of the fundamental theorem on the density of sums of sets ofpositive integers" |
| 1951 | Paul Erdős | for his many papers in thetheory of numbers |
| 1956 | John T. Tate | for his paper "The higher dimensionalcohomology groups ofclass field theory" |
| 1962 | Kenkichi Iwasawa | for his paper "Gamma extensions ofnumber fields" |
| Bernard M. Dwork | for his paper "On the rationality of thezeta function of analgebraic variety" | |
| 1967 | James Ax Simon B. Kochen | for a series of three joint papers "Diophantine problems over local fields I, II, III" |
| 1972 | Wolfgang M. Schmidt | for various papers |
| 1977 | Goro Shimura | for various papers |
| 1982 | Robert P. Langlands | for pioneering work onautomorphic forms,Eisenstein series andproduct formulas |
| Barry Mazur | for outstanding work onelliptic curves andAbelian varieties, especially on rational points of finite order | |
| 1987 | Dorian M. Goldfeld | for his paper "Gauss's class number problem forimaginary quadratic fields" |
| Benedict Gross Don Zagier | for their paper "Heegner points andderivatives ofL-Series" | |
| 1992 | Karl Rubin | for his work in the area ofelliptic curves andIwasawa Theory |
| Paul Vojta | for his work onDiophantine problems | |
| 1997 | Andrew J. Wiles | for his work on theShimura–Taniyama conjecture andFermat's Last Theorem |
| 2002 | Henryk Iwaniec | for his fundamental contributions toanalytic number theory |
| Richard Taylor | for several outstanding advances inalgebraic number theory | |
| 2005 | Peter Sarnak | for his fundamental contributions tonumber theory |
| 2008 | Manjul Bharğava | for his revolutionary work on higher composition laws |
| 2011 | Chandrashekhar Khare Jean-Pierre Wintenberger | for their remarkable proof ofSerre's modularity conjecture |
| 2014 | Yitang Zhang | for his work on boundedgaps between primes |
| Daniel Goldston János Pintz Cem Y. Yildirim | for their work on smallgaps between primes | |
| 2017 | Henri Darmon | for his contributions to the arithmetic of elliptic curves and modular forms. |
| 2020 | James Maynard | for his papers "Small gaps between primes" (Ann. of Math., 2015), "Large gaps between primes"(Ann. of Math., 2016), and "Primes with restricted digits" (Inv. Math., 2019). |
| 2023 | Kaisa Matomäki Maksym Radziwiłł | for their breakthrough paper, "Multiplicative functions in short intervals" (Annals of Math. 183 (2016), pp. 1015-1056) |
| James Newton Jack Thorne | for their astonishing proof of a landmark, sought-after case of the Langlands Conjectures: namely the symmetric power functoriality for holomorphic modular forms (achieved in their two papers: 1. Symmetric power functoriality for holomorphic modular forms, I. Publ. Math. Inst. Hautes Études Sci. 134 (2021), pp. 1-116 2. Symmetric power functoriality for holomorphic modular forms, II. Publ. Math. Inst. Hautes Études Sci. 134 (2021), pp. 117-152) |
For full citations, see external links.