Sylvester Medal

The Sylvester Medal is a bronze medal awarded by the Royal Society (London) for the encouragement of mathematical research, and accompanied by a £1,000 prize.[1] 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.[2][3] Initially awarded every three years with a prize of around £900,[2][4] 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.[1] The award winner is chosen by the Society's A-side awards committee, which handles physical rather than biological science awards.

As of 2019, 43 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. Only two women (Mary Cartwright and Dusa McDuff) have ever won the medal.

List of recipients

Year	Name	Nationality	Rationale^[5]
1901	Henri Poincaré	French	As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics, and celestial mechanics. He was responsible for formulating the Poincaré conjecture, one of the most famous unsolved problems in mathematics, until it was solved in 2002–3. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is also considered to be one of the founders of the field of topology.^[6]^[7]
1904	Georg Cantor	German	Cantor is best known as the inventor of set theory, which has become a fundamental theory in mathematics. He established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. He defined the cardinal and ordinal numbers and their arithmetic.
1907	Wilhelm Wirtinger	Austrian	Wirtinger worked on complex analysis, geometry, algebra, number theory, Lie groups and knot theory; he was honored for his work on the general theory of functions.^[8]
1910	Henry Frederick Baker	British	Baker worked mainly in algebraic geometry, but is also remembered for contributions to partial differential equations (related to what would become known as solitons), and Lie groups. The Medal was awarded in honor of his work with Abelian functions and for his edition of the collected mathematical works of James Joseph Sylvester.^[9]
1913	James Whitbread Lee Glaisher	British	Lee is now remembered mostly for work in number theory that anticipated later interest in the detailed properties of modular forms. He published widely over other fields of mathematics.^[10] In addition to number theory, the Medal was bestowed to acknowledge his work in the theory of elliptic functions.
1916	Jean Gaston Darboux	French	Darboux made several important contributions to geometry and mathematical analysis (see, for example, linear PDEs). His contribution to the differential geometry of surfaces appears in the four volume collection of studies he published between 1887 and 1896.^[11]
1919	Percy Alexander MacMahon	British	MacMahon is especially noted in connection with the partitions of numbers and enumerative combinatorics and received the Medal for this work. His two volume Combinatory analysis, published in 1915/16, is the first major book in enumerative combinatorics. MacMahon also did pioneering work in recreational mathematics and patented several successful puzzles.^[12]
1922	Tullio Levi-Civita	Italian	Levi-Civita made significant contributions in many areas of math, including foundational papers in both pure and applied mathematics, celestial mechanics (notably on the three-body problem) and hydrodynamics. He is most famous for his work on absolute differential calculus (tensor calculus) and its applications to the theory of relativity.^[13] In addition to his research in geometry, inquiries in mechanics led to his receiving the Medal.
1925	Alfred North Whitehead	British	Whitehead received the Medal for his work on the foundations of mathematics, but also wrote on algebra, logic, philosophy of science, physics, metaphysics, and education. He supervised the doctoral dissertations of Bertrand Russell and Willard Van Orman Quine, thus influencing logic and virtually all of analytic philosophy. He co-authored the epochal Principia Mathematica with Russell.^[14]
1928	William Henry Young	British	Young, who was awarded "for his contributions to the theory of functions of a real variable",^[5] worked on measure theory, Fourier series, differential calculus amongst other fields, and made brilliant and long-lasting contributions to the study of functions of several complex variables.^[15]
1931	Edmund Taylor Whittaker	British	Recognized with the Medal for his work in both pure mathematics and applied mathematics, Whittaker also contributed widely to mathematical physics and the theory of special functions. He had a particular interest in numerical analysis, but also worked on celestial mechanics and the history of physics.^[16]
1934	Bertrand Russell	British	A philosopher, logician, mathematician, historian, and social critic,^[17] Russell was honored "for his distinguished work on the foundations of mathematics."^[5]
1937	Augustus Edward Hough Love	British	Love is famous for his work on the mathematical theory of elasticity, which, along with his research into hydro-dynamics, resulted in his receiving the Medal. He worked on wave propagation and developed a mathematical model of surface waves known as Love waves. He contributed to the theory of tidal locking and introduced the parameters known as Love numbers, which are used in problems related to the tidal deformation of the Earth due to the gravitational attraction of the Moon and Sun. He authored the two volume classic, A Treatise on the Mathematical Theory of Elasticity.^[18]^[19]
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 eigen-function 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 Zealand	"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	"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."