# Browse Prizes and Awards

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Frank Nelson Cole Prize in Number Theory 2023 Kaisa Matomäki; Maksym Radziwill; James Newton; Jack Thorne

The 2023 AMS Cole Prize in Number Theory is awarded to Kaisa Matomäki, James Newton, Maksym Radziwill, and Jack Thorne. K. Matomäki and M. Radziwiłł for their breakthrough paper 1. "Multiplicative functions in short intervals" [Annals of Math. 183 (2016), 1015-1056], which together with further developments by themselves and their collaborators have led to the solution and advances on long standing difficult problems, such as the Chowla Conjecture concerning local patterns in the parity of the number of prime factors of an integer. J. Newton and J. Thorne for their astonishing proof of a landmark sought after case of the Langlands Conjectures; namely the symmetric power functoriality for holomorphic modular forms. This is 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.

Prize announcement as seen in the news release.

Frank Nelson Cole Prize in Number Theory 2020 James Maynard

The 2020 Cole Prize in Number Theory is awarded to **James Maynard **for his many contributions to prime number theory. In particular, the prize recognizes the papers

i. "Small gaps between primes" (Ann. of Math., 2015),

ii. "Large gaps between primes"(Ann. of Math., 2016), and

iii. "Primes with restricted digits" (Inv. Math., 2019).

Prize announcement as seen in the news release.

Frank Nelson Cole Prize in Number Theory 2017 Henri Darmon

Eighteenth award: The 2017 Frank Nelson Cole Prize in Number Theory was awarded to Henri Darmon for his contributions to the arithmetic of elliptic curves and modular forms.

Prize announcement as seen in *Notices of the AMS* and in the news release.

Frank Nelson Cole Prize in Number Theory 2014 Yitang Zhang; Cem Yildirim; János Pintz; Daniel Goldston

Eighteenth award: The 2014 Frank Nelson Cole Prize in Number Theory was awarded to Yitang Zhang for his work on bounded gaps between primes and to Cem Y. Yildirim, János Pintz and Daniel Goldston were jointly awarded the 2014 Cole Prize in Number Theory for their work on small gaps between primes.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Number Theory 2011 Chandrashekhar Khare; Jean-Pierre Wintenberger

Seventeenth award: The 2011 Frank Nelson Cole Prize in Number Theory was awarded to Chandrashekhar Khare and Jean-Pierre Wintenberger for their remarkable proof of Serre's modularity conjecture.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Number Theory 2008 Manjul Bhargava

Sixteenth award: The 2008 Frank Nelson Cole Prize in Number Theory Manjul Bhargava for his revolutionary work on higher composition laws.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Number Theory 2005 Peter Sarnak

Fifteenth award: The 2005 Frank Nelson Cole Prize in Number Theory Peter Sarnak for his fundamental contributions to number theory and in particular his book Random Matrices, Frobenius Eigenvalues and Monodromy, written jointly with his Princeton colleague Nicholas Katz.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Number Theory 2002 Henryk Iwaniec; Richard Taylor

Fourteenth award: The 2002 Frank Nelson Cole Prize in Number Theory Henryk Iwaniec for his fundamental contributions to analytic number theory, and to Richard Taylor for several outstanding advances in algebraic number theory.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Number Theory 1997 Andrew J. Wiles

Thirteenth award: The 1997 Frank Nelson Cole Prize in Number Theory Andrew J. Wiles for his work on the Shimura-Taniyama conjecture and Fermat's Last Theorem, published in Modular elliptic curves and Fermat's Last Theorem, Ann. of Math. 141 (1995), 443-551.

Prize announcement as seen in *Notices of the AMS*.

Frank Nelson Cole Prize in Number Theory 1992 Karl Rubin; Paul Vojta

Twelfth award: The 1992 Frank Nelson Cole Prize in Number Theory Karl Rubin for his work in the area of elliptic curves and Iwasawa Theory with particular reference to his papers Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication and The "main conjectures" of Iwasawa theory for imaginary quadratic fields and to Paul Vojta for his work on Diophantine problems with particular reference to his paper Siegel's theorem in the compact case.

Frank Nelson Cole Prize in Number Theory 1987 Dorian M. Goldfeld; Benedict H. Gross; Don B. Zagier

Eleventh award: The 1987 Frank Nelson Cole Prize in Number Theory To Dorian M. Goldfeld for his paper, Gauss's class number problem for imaginary quadratic fields, Bulletin of the American Mathematical Society, volume 13, (1985), pp. 23-37; and to Benedict H. Gross and Don B. Zagier for their paper, Heegner points and derivatives of L-Series, Inventiones Mathematicae, volume 84 (1986), pp. 225-320.

Frank Nelson Cole Prize in Number Theory 1982 Robert P. Langlands; Barry Mazur

Tenth award: The 1982 Frank Nelson Cole Prize in Number Theory Robert P. Langlands for pioneering work on automorphic forms, Eisenstein series and product formulas, particularly for his paper Base change for GL(2), Annals of Mathematics Studies, volume 96, Princeton University Press, 1980; and to Barry Mazur for outstanding work on elliptic curves and Abelian varieties, especially on rational points of finite order, and his paper Modular curves and the Eisenstein ideal, Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques, volume 47 (1977), pp. 33-186.

Frank Nelson Cole Prize in Number Theory 1977 Goro Shimura

Ninth award: The 1977 Frank Nelson Cole Prize in Number Theory Goro Shimura for his two papers, Class fields over real quadratic fields and Heche operators, Annals of Mathematics, Series 2, volume 95 (1972), pp. 130-190; and On modular forms of half integral weight, Annals of Mathematics, Series 2, volume 97 (1973), pp. 440-481.

Frank Nelson Cole Prize in Number Theory 1972 Wolfgang M. Schmidt

Eighth award: The 1972 Frank Nelson Cole Prize in Number Theory Wolfgang M. Schmidt for the following papers: On simultaneous approximation of two algebraic numbers by rationals, Acta Mathematica (Uppsala), volume 119 (1967), pp. 27-50; T-numbers do exist, Symposia Mathematica, volume IV, Academic Press, 1970, pp. 1-26; Simultaneous approximation to algebraic numbers by rationals, Acta Mathematica (Uppsala), volume 125 (1970), pp. 189-201; On Mahler's T-numbers, Proceedings of Symposia in Pure Mathematics, volume 20, American Mathematical Society, 1971, pp. 275-286.

Frank Nelson Cole Prize in Number Theory 1967 Simon B. Kochen; James B. Ax

Seventh award: The 1967 Frank Nelson Cole Prize in Number Theory James B. Ax and Simon B. Kochen for a series of three joint papers, Diophantine problems over local fields. I, II, III, American Journal of Mathematics, volume 87 (1965), pp. 605-630, 631-648, and Annals of Mathematics, Series 2, volume 83 (1966), pp. 437-456.

Frank Nelson Cole Prize in Number Theory 1962 Kenkichi Iwasawa; Bernard M. Dwork

Sixth award: The 1962 Frank Nelson Cole Prize in Number Theory Kenkichi Iwasawa for his paper, Gamma extensions of number fields, Bulletin of the American Mathematical Society, volume 65 (1959), pp. 183-226; and to Bernard M. Dwork for his paper, On the rationality of the zeta function of an algebraic variety, American Journal of Mathematics, volume 82 (1960), pp. 631-648.

Frank Nelson Cole Prize in Number Theory 1956 John T. Tate

Fifth award: The 1956 Frank Nelson Cole Prize in Number Theory John T. Tate for his paper, The higher dimensional cohomology groups of class field theory, Annals of Mathematics, Series 2, volume 56 (1952), pp. 294-297.

Frank Nelson Cole Prize in Number Theory 1951 Paul Erdös

Fourth award: The 1951 Frank Nelson Cole Prize in Number Theory Paul Erdös for his many papers in the theory of numbers, and in particular for his paper, On a new method in elementary number theory which leads to an elementary proof of the prime number theorem, Proceedings of the National Academy of Sciences, volume 35 (1949), pp. 374-385.

Frank Nelson Cole Prize in Number Theory 1946 H. B. Mann

Third award: The 1946 Frank Nelson Cole Prize in Number Theory H. B. Mann for his paper, A proof of the fundamental theorem on the density of sums of sets of positive integers, Annals of Mathematics, Series 2, volume 43 (1942), pp. 523-527.

Frank Nelson Cole Prize in Number Theory 1941 Claude Chevalley

Second award: The 1941 Frank Nelson Cole Prize in Number Theory Claude Chevalley for his paper, La théorie du corps de classes, Annals of Mathematics, Series 2, volume 41 (1940), pp. 394-418.

Frank Nelson Cole Prize in Number Theory 1931 H. S. Vandiver

First award: The 1931 Frank Nelson Cole Prize in Number Theory H. S. Vandiver for his several papers on Fermat's last theorem published in the Transactions of the American Mathematical Society and in the Annals of Mathematics during the preceding five years, with special reference to a paper entitled On Fermat's last theorem, Transactions of the American Mathematical Society, volume 31 (1929), pp. 613-642.