A sum of nearly £900 was subscribed, and it was decided to found a medal and prize for the encouragement and reward of working mathematicians throughout the world. The Council of the Royal Society undertook the trust on condition that the medal should be awarded triennially without regard to nationality.
A bronze medal accompanied by a grant of the balance of the Sylvester Medal Fund, is accordingly awarded triennially for the Encouragement of Mathematical Research.
The winners of the medals are given below.
1901 Henri Poincaré
... for his many and important contributions to mathematical science.
1904 Georg Cantor
... for his brilliant researches in the theories of aggregates and of sets of points of the arithmetic continuum, of transfinite numbers, and Fouriers series.
1907 Wilhelm Wirtinger
... for his contributions to the general theory of functions.
1910 Henry F Baker
... for his researches in the theory of Abelian functions and for his edition of Sylvesters Collected Works.
1913 James W L Glaisher
... for his mathematical researches, especially those in connection with the theory of numbers and the theory of elliptic functions.
1916 Jean G Darboux
... for his distinguished contributions to mathematical science.
1919 Percy A MacMahon
... for his researches in pure mathematics, especially in connection with the partition of numbers and analysis.
1922 Tullio Levi-Civita
... for his researches in geometry and mechanics.
1925 Alfred N Whitehead
... for his researches on the foundations of mathematics.
1928 William H Young
... for his contributions to the theory of functions of a real variable.
1931 Edmund T Whittaker
... for his original contributions to both pure and applied mathematics.
1934 Bertrand Russell
... for his distinguished work on the foundations of mathematics.
1937 Augustus E H Love
... for his researches in classical mathematical physics, particularly the mathematical theories of elasticity and hydro-dynamics.
1940 Geoffrey H Hardy
... for his important contributions to many branches of pure mathematics.
1943 John E Littlewood
... for his mathematical discoveries and supreme insight in the analytical theory of numbers.
1946 George N Watson
... for his distinguished contributions to pure mathematics in the field of mathematical analysis and in particular for his work on asymptotic expansion and on general transforms.
1949 Louis J Mordell
... for his distinguished researches in pure mathematics, especially for his discoveries in the theory of numbers.
1952 Abram S Besicovitch
... for his outstanding work on almost-periodic functions, the theory of measure and integration and many other topics of theory of functions.
1955 Edward C Titchmarsh
... for his distinguished researches on the Riemann zeta-function, analytical theory of numbers, Fourier analysis, and eigen-function expansions.
1958 Max H A Newman
... for his distinguished contributions to combinatory topology, Boolean algebras and mathematical logic.
1961 Philip Hall
... for his distinguished researches in algebra.
1964 Mary L Cartwright
... for her distinguished contributions to analysis and the theory of functions of a real and complex variable.
1967 Harold Davenport
... for his many distinguished contributions to the theory of numbers.
1970 George F J Temple
... for his many distinguished contributions to applied mathematics, especially in his work on distribution theory.
1973 John W S Cassels
... for his numerous important contributions to the theory of numbers.
1976 David G Kendall
... for his many distinguished contributions to probability theory and its applications.
1979 Graham Higman
... for his distinguished and profoundly influential contributions to the theory of finite and infinite groups.
1982 John Frank Adams
... for his solution of several outstanding problems of algebraic topology and of the methods he invented for this purpose which have proved of prime importance in the theory of the subject.
1985 John G Thompson
... for his fundamental contributions leading to the complete classification of all finite simple groups.
1988 Charles T C Wall
... for his contributions to the topology of manifolds and related topics in algebra and geometry.
1991 Klaus Roth
... for his many contributions to number theory and in particular his solution of the famous problem concerning approximating algebraic numbers by rationals.
1994 Peter Whittle
...for his major distinctive contributions to time series analysis, to optimisation theory, and to a wide range of topics in applied probability theory and the mathematics of operational research.
1997 Harold Coxeter
... for his achievements in geometry, notably projective geometry, non-euclidean geometry and the analysis of spatial shapes and patterns, and for his substantial contributions to practical group-theory which pervade much modern mathematics.
2000 Nigel James Hitchin
... for his important contributions to many parts of differential geometry combining this with complex geometry, integrable systems and mathematical physics interweaving the most modern ideas with the classical literature.
2003 Lennart Carleson
... for his deep and fundamental contributions to mathematics in the field of analysis and complex dynamics. His most spectacular achievement was the proof of the convergence almost everywhere of the Fourier Series of square integrable and continuous functions.
2006 Peter Swinnerton-Dyer
... for his fundamental work in arithmetic geometry and his many contributions to the theory of ordinary differential equations.
2009 John Ball
... for his seminal work in mechanics and nonlinear analysis and his encouragement of mathematical research in developing countries.
2010 Graeme Segal
... for his highly influential and elegant work on the development of topology, geometry and quantum field theory, bridging the gap between physics and pure mathematics
2012 John Toland
... or his original theorems and remarkable discoveries in nonlinear partial differential equations, including applications to water waves.
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