The

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".

... for his paper "La théorie du corps de classes".

... for his paper "A proof of the fundamental theorem on the density of sums of sets of positive integers".

... 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".

... for his paper "The higher dimensional cohomology groups of class field theory".

... for his paper "Gamma extensions of number fields".

... for his paper "On the rationality of the zeta function of an algebraic variety".

... for a series of three joint papers "Diophantine problems over local fields. I, II, III".

... 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".

... for his two papers "Class fields over real quadratic fields and Hecke operators" and "On modular forms of half integral weight".

... for pioneering work on automorphic forms, Eisenstein series and product formulas, particularly for his paper "Base change for GL(2)".

... 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".

... for his paper "Gauss's class number problem for imaginary quadratic fields".

... for their paper "Heegner points and derivatives of L-Series".

... 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".

... for his work on Diophantine problems with particular reference to his paper "Siegel's theorem in the compact case".

... for his work on the Shimura-Taniyama conjecture and Fermat's Last Theorem, published in "Modular elliptic curves and Fermat's Last Theorem".

... for his fundamental contributions to analytic number theory.

... for several outstanding advances in algebraic number theory.

... 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.

... for his revolutionary work on higher composition laws.

... for their remarkable proof of Serre's modularity conjecture.

... for his work on bounded gaps between primes

... for their work on small gaps between primes.

... for his contributions to the arithmetic of elliptic curves and modular forms.

History of the AMS

Presidents of the AMS

AMS Colloquium Lecturers

AMS Gibbs Lecturers

**AMS Prizes:**

AMS/SIAM Birkhoff Prize

AMS Bôcher Prize

AMS Cole Prize in Algebra

AMS Cole Prize in Number Theory

AMS Conant Prize

AMS Fulkerson Prize

AMS Satter Prize

AMS Steele Prize

AMS Veblen Prize

AMS Wiener Prize

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JOC/EFR February 2019

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