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.[1] 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.[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 to L. E. Dickson, while the first award for number theory was made in 1931 to H. S. Vandiver.[2]

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"
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"
Richard G. Swan for his paper "Groups of cohomological dimension one"
1975 Hyman Bass for his paper "Unitary algebraic K-theory"
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"
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
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"
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
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"
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
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
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
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)
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.

See also


  1. ^ a b Richardson, R. G. (1930), "The Society's Prizes", Bulletin of the American Mathematical Society, 36: 3–4, doi:10.1090/S0002-9904-1930-04851-X.
  2. ^ a b Pitcher, Everett (1988), A history of the second fifty years, American Mathematical Society 1939-88, American Mathematical Society, pp. 51–54, ISBN 9780821896761.