The 2001 Clay Research Award to Edward Witten recognizes, "a lifetime of achievement, especially for pointing the way to unify apparently disparate fields of mathematics and to discover their elegant simplicity through links with the physical world." A native of Baltimore, Maryland, Witten is Professor at the Institute for Advanced Study in Princeton. Trained as a physicist, Witten became well-known for his discovery of new instanton solutions to the Yang-Mills equations and for relating super-symmetric quantum mechanics to Morse theory and index theory. For the past fifteen years, he has also remained the leading exponent of string theory and related efforts to unify the four fundamental forces of nature into one mathematical picture. Witten's work has greatly influenced mathematics. He demonstrated that the Jones invariant of knots could be computed as the statistical average value of an operator representing parallel transport around the knot, with the statistical weight given by a particular gauge theory action. For this insight he received the Fields Medal in 1990. Eleven years later Witten continues to surprise the scientific community with his proposal to unify five separate string theories into one "master theory" dubbed "M-theory."
Other highlights of Witten's work include his proof of the positivity of energy in classical relativity, his interpretation of unusual symmetries in physics, including mirror symmetry and SL(2,Z) invariance, his proposals leading to the discovery of new rigidity theorems, and his picture of invariants in low dimensional topology and geometry, including the discovery of the Seiberg-Witten equations and their relation to geometry.
The early contributions of Witten are summarized in: Michael Atiyah, On the work of Edward Witten, Proceedings of the International Congress of Mathematicians, Kyoto, 1990 I (Tokyo, 1991), 31-35 L D Faddeev, On the work of Edward Witten, Addresses on the works of Fields medalists and Rolf Nevanlinna Prize winner (Tokyo, 1990).
References and ideas to some of his more recent contributions can be found in the following: Edward Witten. Monopoles and Four-Manifolds, Math.Res.Lett. 1 (1994) 769-796.
Nathan Seiberg, Edward Witten. String Theory and Non-commutative Geometry, Journal of High Energy Physics 9909 (1999) 032.
Edward Witten. Overview Of K-Theory Applied To Strings, Int.J.Mod.Phys. A16 (2001) 693-706.
Edward Witten. Anti-de Sitter Space And Holography, Adv.Theor.Math.Phys. 2 (1998) 253-291.