Sylvester Medal

The Sylvester Medal is a bronze medal awarded by the Royal Society for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian Professor of Geometry at the University of Oxford in the 1880s, and first awarded in 1901, having been suggested by a group of Sylvester's friends (primarily Raphael Meldola) after his death in 1897. Initially awarded every three years with a prize of around £900, the Royal Society have announced that starting in 2009 it will be awarded every two years instead, and is to be aimed at 'early to mid career stage scientist' rather than an established mathematician. The award winner is chosen by the Society's A-side awards committee, which handles physical rather than biological science awards.

Sylvester Medal
James Joseph Sylvester, after whom the award is named
Awarded for	"outstanding contributions in the field of mathematics"
Date	1901 (1901)
Country	United Kingdom
Presented by	Royal Society
Website	https://royalsociety.org/medals-and-prizes/sylvester-medal/

As of 2021, 45 medals have been awarded, of which all but 10 have been awarded to citizens of the United Kingdom, two to citizens of France and United States, and one medal each has been won by citizens of New Zealand, Germany, Austria, Russia, Italy, Sweden and South Africa. As of 2021 three women have won the medal, Mary Cartwright in 1964, Dusa McDuff in 2018, and Frances Kirwan in 2021.

List of recipients

List of recipients of the Sylvester Medal

Year	Portrait	Name	Nationality	Rationale	Notes
1901		Henri Poincaré	French	"For his many and important contributions to mathematical science."
1904		Georg Cantor	German	"For his researches in the theories of aggregates and of sets of points of the arithmetic continuum, of transfinite numbers, and Fourier's series."
1907		Wilhelm Wirtinger	Austrian	"For his contributions to the general theory of functions."
1910		Henry Frederick Baker	British	"For his researches in the theory of Abelian functions and for his edition of Sylvester's 'Collected Works'"
1913		James Whitbread Lee Glaisher	British	"For his mathematical researches."
1916		Jean Gaston Darboux	French	"For his contributions to mathematical science."
1919		Percy Alexander MacMahon	British	"For his researches in pure mathematics, especially in connection with the partition of numbers and analysis"
1922		Tullio Levi-Civita	Italian	"For his researches in geometry and mechanics"
1925		Alfred North Whitehead	British	"For his researches on the foundations of mathematics"
1928		William Henry Young	British	"For his contributions to the theory of functions of a real variable"
1931		Edmund Taylor Whittaker	British	"For his original contributions to both pure and applied mathematics"
1934		Bertrand Russell	British	"For his distinguished work on the foundations of mathematics"
1937		Augustus Edward Hough Love	British	"In recognition of his researches in classical mathematical physics"
1940		Godfrey Harold Hardy	British	"For his important contributions to many branches of pure mathematics."
1943		John Edensor Littlewood	British	"For his mathematical discoveries and supreme insight in the analytical theory of numbers."
1946	—	George Neville Watson	British	"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 Joel Mordell	British	"For his distinguished researches in pure mathematics, especially for his discoveries in the theory of numbers."
1952	—	Abram Samoilovitch Besicovitch	Russian	"For his outstanding work on almost-periodic functions, the theory of measure and integration and many other topics of theory of functions."
1955	—	Edward Charles Titchmarsh	British	"For his distinguished researches on the Riemann zeta-function, analytical theory of numbers, Fourier analysis, and eigenfunction expansions."
1958		Max Newman	British	"for his distinguished contributions to combinatory topology, Boolean algebras and mathematical logic."
1961		Philip Hall	British	"For his distinguished researches in algebra."
1964		Mary Cartwright	British	"For her distinguished contributions to analysis and the theory of functions of a real and complex variable."
1967		Harold Davenport	British	"For his many distinguished contributions to the theory of numbers."
1970	—	George Frederick James Temple	British	"For his many distinguished contributions to applied mathematics, especially in his work on distribution theory."
1973	—	John William Scott Cassels	British	"For his numerous important contributions to the theory of numbers."
1976		David George Kendall	British	"For his many distinguished contributions to probability theory and its applications."
1979		Graham Higman	British	"For his distinguished and profoundly influential contributions to the theory of finite and infinite groups.
1982		John Frank Adams	British	"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 Griggs Thompson	American	"For his fundamental contributions leading to the complete classification of all finite simple groups."
1988		Charles T. C. Wall	British	"For his contributions to the topology of manifolds and related topics in algebra and geometry."
1991		Klaus Friedrich Roth	British	"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	New Zealander	"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 Scott MacDonald Coxeter	British   Canadian	"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	British	"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	Swedish	"For his deep and fundamental contributions to mathematics in the field of analysis and complex dynamics."
2006		Peter Swinnerton-Dyer	British	"For his fundamental work in arithmetic geometry and his many contributions to the theory of ordinary differential equations."
2009		John M. Ball	British	"For his seminal work in mechanics and nonlinear analysis and his encouragement of mathematical research in developing countries."
2010		Graeme Segal	British	"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 Francis Toland	British   Irish	"For his original theorems and remarkable discoveries in nonlinear partial differential equations, including applications to water waves."
2014		Ben Green	British	"For his famous result on primes in arithmetic progression, and his subsequent proofs of a number of spectacular theorems over the last five to ten years."
2016		Timothy Gowers	British	"For his groundbreaking results in the theory of Banach spaces, pure combinatorics, and additive number theory."
2018		Dusa McDuff	British	"For leading the development of the new field of symplectic geometry and topology."
2019		Peter Sarnak	American   South African	"For transformational contributions across number theory, combinatorics, analysis and geometry."
2020		Bryan John Birch	British	"For driving the theory of elliptic curves, through the Birch-Swinnerton-Dyer conjecture and the theory of Heegner points."
2021		Frances Kirwan	British	"For her research on quotients in algebraic geometry, including links with symplectic geometry and topology, which has had many applications."
2022		Roger Heath-Brown	British	"For his many important contributions to the study of prime numbers and solutions to equations in integers."
2023		Miles Reid	British	"For his exceptionally creative research and fundamental insights into higher-dimensional algebraic geometry, in particular the minimal model program for 3-folds, and for untiring work for the community of algebraic geometers."
2024		Philip Maini	British	"For his contributions to mathematical biology, especially the interdisciplinary modelling of biomedical phenomena and systems."
2025		Martin Hairer	British	"For profound contributions to the fields of probability and analysis, as one of the leading figures in stochastic partial differential equations."

See also

• Awards, lectures and medals of the Royal Society
• List of mathematics awards