Frank Nelson Cole Prize in Number Theory of the AMS

The Frank Nelson Cole Prize in Algebra and the Frank Nelson Cole Prize in Number Theory were founded in honour of Professor Frank Nelson Cole on the occasion of his retirement as secretary of the American Mathematical Society after twenty-five years of service and as editor-in-chief of the Bulletin of the American Mathematical Society for twenty-one years.

The original fund was donated by Professor Cole from money presented to him on his retirement, was augmented by contributions from members of the Society, and was later doubled by his son, Charles A Cole.

The present award is $5,000. The prizes were awarded at two different five-year intervals for contributions to algebra and the theory of numbers, but the intervals have been reduced to three years. The award is for a notable research memoir in analysis that has appeared during the past six years in a recognized North American journal and only members of the American Mathematical Society are eligible.

1931 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".
1941 Claude Chevalley
... for his paper "La théorie du corps de classes".
1946 H B Mann
... for his paper "A proof of the fundamental theorem on the density of sums of sets of positive integers".
1951 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".
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 B Ax and Simon B Kochen
... for a series of three joint papers "Diophantine problems over local fields. I, II, III".
1972 Wolfgang M. Schmidt
... for the papers "On simultaneous approximation of two algebraic numbers by rationals", "T-numbers do exist", "Simultaneous approximation to algebraic numbers by rationals" and "On Mahler's T-numbers".
1977 Goro Shimura
... for his two papers "Class fields over real quadratic fields and Hecke operators" and "On modular forms of half integral weight".
1982 Robert P Langlands
... for pioneering work on automorphic forms, Eisenstein series and product formulas, particularly for his paper "Base change for GL(2)".
1982 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".
1987 Dorian M Goldfeld
... for his paper "Gauss's class number problem for imaginary quadratic fields".
1987 Benedict H Gross and Don B 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 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".
1992 Paul Vojta
... for his work on Diophantine problems with particular reference to his paper "Siegel's theorem in the compact case".
1997 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".
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 and in particular his book "Random Matrices, Frobenius Eigenvalues and Monodromy", written jointly with his Princeton colleague Nicholas Katz.
2008 Manjul Bhargava
... for his revolutionary work on higher composition laws.
2011 Chandrashekhar Khare and Jean-Pierre Wintenberger
... for their remarkable proof of Serre's modularity conjecture.
2014 Yitang Zhang
... for his work on bounded gaps between primes
Cem Y Yildirim, János Pintz and Daniel Goldston
... 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 many contributions to prime number theory.

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