# Winners of the Sylvester Medal of the Royal Society of London

Soon after the death of Professor J J Sylvester, F.R.S., in 1897, a number of his friends considered the advisability of funding some suitable honour of his name and life-work. The suggestion met with a ready response from all parts of the world, and a representative International Comittee was formed.

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

The winners of the medals are given below.

... 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.

Fellows of the Royal Society

Presidents of the Royal Society

Royal Medal

Sylvester Medal

Copley Medal

Bakerian Lectures

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.***2014**Ben Green... 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*... for his groundbreaking results in the theory of Banach spaces, pure combinatorics, and additive number theory.*

**2018**Dusa McDuff*... for leading the development of the new field of symplectic geometry and topology.*

**2019**Peter Sarnak*... for transformational contributions across number theory, combinatorics, analysis and geometry.*

**2020**Bryan John Birch*... for driving the theory of elliptic curves, through the Birch-Swinnerton-Dyer conjecture and the theory of Heegner points.*

**2021**Frances Kirwan*... for her research on quotients in algebraic geometry, including links with symplectic geometry and topology, which has had many applications.*

**2022**Roger Heath-Brown*... for his many important contributions to the study of prime numbers and solutions to equations in integers.***2023**Miles Reid*... 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.*#### MacTutor links:

Royal Society of LondonFellows of the Royal Society

Presidents of the Royal Society

Royal Medal

Sylvester Medal

Copley Medal

Bakerian Lectures