# Cole Prize

The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank 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.
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 to L. E. Dickson, while the first award for number theory was made in 1931 to H. S. Vandiver.

## Frank Nelson Cole Prize in Algebra

| Year | Prizewinner | Citation |
| 1928 | Leonard E. Dickson | for his book "Algebren und ihre Zahlentheorie" |
| 1939 | Abraham Adrian Albert | for his papers on the construction of Riemann matrices |
| 1944 | Oscar Zariski | for four papers on algebraic varieties |
| 1949 | Richard Brauer | for his paper "On Artin's L-series with general group characters" |
| 1954 | Harish-Chandra | for his papers on representations of semisimple Lie algebras and groups |
| 1960 | Serge Lang | for his paper "Unramified class field theory over function fields in several variables" |
| 1960 | 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 "On torsion-free groups with infinitely many ends" |
| 1970 | Richard G. Swan | for his paper "Groups of cohomological dimension one" |
| 1975 | Hyman Bass | for his paper "Unitary algebraic K-theory" |
| 1975 | Daniel G. Quillen | for his paper "Higher algebraic K-theories" |
| 1980 | Michael Aschbacher | for his paper "A characterization of Chevalley groups over fields of odd order" |
| 1980 | Melvin Hochster | for his paper "Topics in the homological theory of commutative rings" |
| 1985 | George Lusztig | for his fundamental work on the representation theory of finite groups of Lie type |
| 1990 | Shigefumi Mori | for his outstanding work on the classification of algebraic varieties |
| 1995 | Michel Raynaud David Harbater | for their solution of Abhyankar's conjecture |
| 2000 | Andrei Suslin | for his work on motivic cohomology |
| 2000 | Aise Johan de Jong | for his important work on the resolution of singularities by generically finite maps |
| 2003 | Hiraku Nakajima | for his work in representation theory and geometry |
| 2006 | János Kollár | for his outstanding achievements in the theory of rationally connected varieties and for his illuminating work on a conjecture of Nash |
| 2009 | Christopher Hacon James McKernan | for their groundbreaking joint work on higher dimensional birational algebraic geometry |
| 2012 | Alexander Merkurjev | for his work on the essential dimension of groups |
| 2015 | Peter Scholze | for his work on perfectoid spaces which has led to a solution of an important special case of the weight-monodromy conjecture of Deligne |
| 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”. |

## Frank Nelson Cole Prize in Number Theory

| Year | Prizewinner | Citation |
| 1931 | Harry Vandiver | for his several papers on Fermat'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 of positive integers" |
| 1951 | Paul Erdős | for his many papers in the theory of numbers |
| 1956 | John T. Tate | for his paper "The higher dimensional cohomology groups of class field theory" |
| 1962 | Kenkichi Iwasawa | for his paper "Gamma extensions of number fields" |
| 1962 | Bernard M. Dwork | for his paper "On the rationality of the zeta function of an algebraic 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 on automorphic forms, Eisenstein series and product formulas |
| 1982 | Barry Mazur | for outstanding work on elliptic curves and Abelian varieties, especially on rational points of finite order |
| 1987 | Dorian M. Goldfeld | for his paper "Gauss's class number problem for imaginary quadratic fields" |
| 1987 | Benedict Gross Don Zagier | for their paper "Heegner points and derivatives of L-Series" |
| 1992 | Karl Rubin | for his work in the area of elliptic curves and Iwasawa Theory |
| 1992 | Paul Vojta | for his work on Diophantine problems |
| 1997 | Andrew J. Wiles | for his work on the Shimura–Taniyama conjecture and Fermat's Last Theorem |
| 2002 | Henryk Iwaniec | for his fundamental contributions to analytic number theory |
| 2002 | Richard Taylor | for several outstanding advances in algebraic number theory |
| 2005 | Peter Sarnak | for his fundamental contributions to number theory |
| 2008 | Manjul Bharğava | for his revolutionary work on higher composition laws |
| 2011 | Chandrashekhar Khare Jean-Pierre Wintenberger | for their remarkable proof of Serre's modularity conjecture |
| 2014 | Yitang Zhang | for his work on bounded gaps between primes |
| 2014 | Daniel Goldston János Pintz Cem Y. Yildirim | for their work on small gaps 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) |
| 2023 | 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.