The Frederic Esser Nemmers Prize in Mathematics

2008: Simon Donaldson

2006: Robert P. Langlands

2004: Mikhael L. Gromov

2002: Yakov G. Sinai

2000: Edward Witten

1998: John H. Conway

1996: Joseph B. Keller

1994: Yuri I. Manin

Simon Donaldson
Recipient, 2008 Frederic Esser Nemmers Prize in Mathematics

Simon Donaldson is the Royal Society Research Professor at Imperial College, London. The selection committee for the mathematics prize recognized Donaldson for his “groundbreaking work in four-dimensional topology, symplectic geometry and gauge theory, and for his remarkable use of ideas from physics to advance pure mathematics.”

“Donaldson's breakthrough work developed new techniques in the geometry of four-manifolds and the study of their smooth structures,” said John Franks, professor and chair of mathematics at Northwestern.  “His methods,” Franks continued, “have been described as extremely subtle, using difficult nonlinear partial differential equations.  Using instantons, solutions to the equations of Yang-Mills gauge theory, he gained important insight into the structure of closed four-manifolds. Gauge theory techniques also enabled him to show the existence of four-manifolds with no smooth structure and others with infinitely many.  His work has provided the seminal steps for the work of others in study of four-manifolds.”

More recently, Donaldson has made fundamental contributions to the understanding of symplectic manifolds, the phase-spaces of classical mechanics, and he shows that a surprisingly large part of the theory of algebraic geometry extends to them.

His two books and more than 60 published papers are widely recognized for their originality as well as their elegance and clarity.

Donaldson received his B.A at Cambridge University and his D.Phil. from Oxford University.  In 1986, only three years after completion of his doctorate, he was elected a fellow of the Royal Society.  That same year he received the Fields Medal, widely recognized as the most prestigious honor for a mathematician under the age of 40. He was awarded the Royal Medal of the Royal Society in 1992, the Crafoord Prize in 1994, and the King Faisal Prize in 2006.  In 2000 he was elected a foreign associate of the National Academy of Sciences.

Click here for press release on Simon Donaldson's receipt of the award.

Top of Page

Robert P. Langlands
Recipient, 2006 Frederic Esser Nemmers Prize in Mathematics

Robert P. Langlands is Hermann Weyl Professor of Mathematics at the Institute for Advanced Study, Princeton, New Jersey. The selection committee for the mathematics prize recognized Langlands for his “fundamental vision connecting representation theory, automorphic forms and number theory.”

Langlands is best known for the fundamental research program that bears his name. “This program postulates a deep relationship between two different areas of mathematics, number theory and automorphic forms, via a study of their symmetries,” said Kari Vilonen, professor of mathematics at Northwestern.

“Since its initiation about 40 years ago, the Langlands program has served as a unifying principle in mathematics and has guided research in number theory, automorphic forms and representation theory,” he said. “Recently, it also had entered mathematical physics. It remains a research program for the future in all these areas.”

Langlands’ numerous distinguished awards include the La Grande Medaille d’or de l’Academie (2000), the Wolf Prize in Mathematics (1995-96), the National Academy of Sciences Medal (1993) and the Cole Prize (1982). He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences.

Langlands is the author or co-author of numerous articles and the editor, with D. Ramakrishnan, of “The Zeta Functions of Picard Modular Surfaces,” Les Publications CRM, Montreal (1992).

Top of Page

Mikhael L. Gromov
Recipient, 2004 Frederic Esser Nemmers Prize in Mathematics

The Selection Committee for the mathematics prize recognized Gromov "for his work in Riemannian geometry, which revolutionized the subject; his theory of pseudoholomorphic curves in symplectic manifolds; his solution of the problem of groups of polynomial growth; and his construction of the theory of hyperbolic groups." His work has been revolutionary in a number of basic areas of modern geometry.

Reflecting his extraordinary creativity, Gromov’s work is both elegant and immediately relevant to problems in applied mathematics and mathematical physics. Gromov's work on symplectic manifolds has played a central role in the development of string theory, one of the most promising unified field theories of theoretical physics. He is a true successor to great geometers of the past, such as Felix Klein, who lectured at Northwestern in 1893.

Gromov is the recipient of numerous distinguished awards, including the Kyoto Prize (2002), the Balzan Prize (1999), the Leroy P. Steele Prize (1997), the Lobatchewski Medal (1997), the Wolf Prize (1993), the Prix UAP (1989), Elie Cartan Prize (1984), Oswald Veblen Prize in Geometry (1981), and the Moscow Mathematical Society Prize (1971). He also holds an honorary doctorate from the University of Geneva (1992). He was invited to give addresses to four International Conferences of Mathematicians, including a plenary lecture in 1986.

He is an overseas member of the National Academy of Sciences, The American Academy of Arts and Sciences and a member of the Academy of Sciences (Paris).

Before joining the Institut des Hautes Études Scientifiques in 1982, Gromov was a member of the faculty at Leningrad University, the State University of New York at Stony Brook and the Universite de Paris VI. He obtained his master’s, doctorate and state doctor’s degree from Leningrad University.

Top of Page

Yakov G. Sinai
Recipient, 2002 Frederic Esser Nemmers Prize in Mathematics

Yakov G. Sinai, professor of mathematics at Princeton University since 1993, is internationally regarded as a pioneer in the field of dynamical systems. His work has revolutionized the study of dynamical systems and influenced statistical mechanics, probability theory and statistical physics.

Sinai's work deals with measuring dynamical systems, or systems that change over time, such as weather, the motion of planets and economic systems. These systems can be accurately measured in the short term (short term being relative to the issue at hand); but when analyzed in the long term, the systems are difficult to understand and predict. Sinai was the first to come up with a mathematical foundation for determining the number that defines the complexity of a given dynamical system. His mathematical system is called Kolmogorov-Sinai entropy.

Sinai received his bachelor's, master's and doctorate degrees from Moscow State University. He also held several positions with Moscow State University, including researcher with the Laboratory of Probabilistic and Statistical Methods (1971-present) and professor of mathematics (1971-93). In addition, Sinai has served as a senior researcher at the Landau Institute of Theoretical Physics, Academy of Sciences.

Sinai's contributions have been recognized by numerous organizations. He has been the recipient of several awards and honors, including memberships in the Russian, U.S. and Hungarian Academies of Science, and an honorary membership in the London Mathematics Society. Other awards include the Thomas Jones Professor of Princeton University, Wolfe Foundation Prize in Mathematics, Doctor Honoris Causa of Warsaw University, Markov Prize, Heineman Prize and Boltzman Gold Medal.

Sinai has been an invited speaker at several important international conferences. He has spoken four times at the International Congress of Mathematics and has delivered lectures at Harvard University and the Hebrew University of Jerusalem.

Top of Page

Edward Witten
Recipient, 2000 Frederic Esser Nemmers Prize in Mathematics

Edward Witten is professor of physics at the Institute for Advanced Study in Princeton.

Witten is regarded as the world’s premier theoretical physicist. Known for his many contributions to particle physics and string theory, he has almost single-handedly constructed a new branch of mathematical physics.

He is a leading scholar in the field of superstring theoryÑwhich seeks to describe all the fundamental forces of nature in one conceptual framework. The theory suggests that the basic building blocks of nature are not tiny particles but small loops and snippets of what resembles string. He has also proposed an extension of string physics, “M-Theory,” to unify the five separate string theories into one “master” theory.

Witten’s work on the related idea of topological quantum field theory — which allows physicists to find connections between seemingly unrelated equationsÐtogether with many achievements in mathematics inspired by insights from physics earned Witten the prestigious Fields Medal in 1990, the highest honor awarded to a mathematician under age 40.

Although a physicist, Witten’s command of mathematics is rivaled by few mathematicians. By interpreting physical ideas in mathematical form, he has applied physical insight that has led to new and deep mathematical theorems.

Witten’s ideas have triggered major mathematical developments by the force of their vision and conceptual clarity, with his main discoveries becoming theorems.

His work on supersymmetry and Morse theory has become of central importance in the study of differential geometry. Witten is the leading theorist on the most enigmatic problem of theoretical physics — the mathematical incompatibility of the foundation pillars of quantum mechanics and the General Theory of Relativity.

Witten served as a professor of physics at Princeton from 1980-87 when he joined the Institute for Advanced Study. He received a MacArthur Fellowship in 1982 and in 1985 received the Einstein Medal from the Einstein Society and the Physical and Mathematics Science Award from the New York Academy of Science.

In 1996 Time magazine profiled him as one of the 25 most influential people in America.

Witten, currently on leave at the California Institute of Technology, is regarded as the world’s premier theoretical physicist. Known for his many contributions to particle physics and string theory, he has almost single-handedly constructed a new branch of mathematical physics.

Top of Page

John H. Conway
Recipient, 1998 Frederic Esser Nemmers Prize in Mathematics

John H. Conway is von Neumann Professor of Mathematics at Princeton University.

Conway, one of the preeminent theorists in the study of finite groups (the mathematical abstraction of symmetry) and one of the world's foremost knot theorists, is the author of more than 10 books and more than 130 journal articles on a wide variety of mathematical subjects. He has also done path-breaking work in number theory, game theory, coding theory, tiling, and the creation of new number systems. The system of "Surreal Numbers" which he invented is the subject of a popular book by computer scientist Donald Knuth.

Beyond the academic world Conway is widely known as the inventor of the "Game of Life," a computer simulation of simple cellular "life," governed by remarkably simple rules which give rise to amazingly complex behavior. It was popularized by Martin Gardner's columns in Scientific American in the early 1970s and has had a large number of devotees ever since.

Conway may well have the distinction of having more books, articles and Web pages devoted to his creations than any other living mathematician.

Conway was educated at Cambridge University and served as a professor of mathematics there prior to joining Princeton in 1986. He is a Fellow of the Royal Society and received of the Polya Prize of the London Mathematical Society.

Top of Page

Joseph B. Keller
Recipient, 1996 Frederic Esser Nemmers Prize in Mathematics

Joseph B. Keller, Lewis M. Terman Professor of Mathematics and Mechanical Engineering at Stanford University, is regarded by many as the world's most distinguished applied mathematician. He was awarded the National Medal of Science by the National Academy of Sciences in 1988 and is a member of the Royal Society, the National Academy of Sciences and the American Academy of Arts and Sciences.

Keller originated the Geometrical Theory of Diffraction to solve problems of wave propagation. The theory is an indispensable tool for engineers and scientists working on radar, the design of antennas and on high frequency systems in complicated environments. He also formulated methods to solve the problems of wave propagation through heterogeneous, turbulent, or random media in which fluctuations occur due to the irregular and fluctuating properties of the medium.

Keller has worked extensively on problems related to national security, including sonar, underwater explosions, atmospheric explosions of hydrogen bombs, and A-bomb explosions on ships and submarines. The author of more than 400 scientific papers, he twice received the Lester R. Ford Award for expository writing from the Mathematical Association of America.

Keller has trained generations of mathematicians, scientists, and engineers in what is called the Keller School of Applied Mathematics, which centers on the intricacy and beauty of mathematical modeling and analysis of physical phenomena.

Keller received bachelor's, master's and Ph.D. degrees from New York University, where he was a professor for 30 years. He also held positions at Princeton University and Columbia University. He has been a professor at Stanford since 1978 and a research associate at the Woods Hole Oceanographic Institution since 1969.

Top of Page

Yuri I. Manin
Recipient, 1994 Frederic Esser Nemmers Prize in Mathematics

Yuri I. Manin is a scientific member of the Max Planck Institute for Mathematics, Bonn, Germany, and Steklov Mathematical Institute, Moscow, Russia.

Manin is widely regarded as one of the outstanding mathematicians of the 20th century and his work spans such diverse branches of mathematics as algebraic geometry, number theory, and mathematical physics.

He enriched these fields by numerous fundamental contributions, including the solution of major problems and the development of techniques that opened new avenues of research.

In his 1963 proof of the Mordell conjecture for function fields, Manin introduced what is now known as Gauss-Manin connection, an indispensable tool in modern algebraic geometry in its own right. In 1971, Manin (with Iskovskih) found counter-examples to the longstanding problem of Luroth concerning rational uniformization of algebraic loci.

Manin's work in number theory, especially in p-adic analysis and theory modular forms, drew intuition from geometry and used "continuous" techniques to attack fundamental arithemetic problems. His study of Diophantine equations led to the discovery of new asymptotic properties of their solutions and a new obstruction for their solvability (Brauer-Manin obstruction).

Among Manin's many contributions to mathematical physics is the classification of instantons, the solutions of field equations describing microscopic quantum fluctuations of the vacuum. His 1978 work on this problem (with Drinfiled), besides being of fundamental importance in physics, laid the foundation for the recent progress in the purely mathematical study of 4-mainfolds. He has also done important work on Hamiltonian structure of completely integrable wave equations, construction of algebro-geometric solutions of Yang-Mills-Dirac equations, string theory, and quantum groups.

A native of Simferopol, Russia, Manin received a bachelor's degree from Moscow State University in 1958 and a Ph.D. from the Steklov V.A. Institute of Mathematics in Moscow in 1960. He held a chair in mathematics at Moscow State University from 1965-1991.

Manin was a visiting professor at several universities, including Harvard University, Massachusetts Institute of Technology, and Columbia University from 1991-1993, when he became associated with the Max Planck Institute for Mathematics. He is also the author or co-author of ten monographs and more than 150 papers.

Manin has been the recipient of numerous awards, including the Brouwer Gold Medal in 1987 for his work in number theory and a Lenin Prize in 1967 for work in algebraic geometry. He is a corresponding member of the Russian Academy of Sciences, a foreign member of the Royal Netherlands Academy of Arts and Sciences, and a member of Academic Europaea.

Top of Page