ITHACA, N.Y. -- William P. Thurston, professor of mathematics at Cornell University and a world-renowned mathematician in the area of topology, has won the 2005 American Mathematical Society (AMS) Book Prize. The award, which is given every three years, recognizes "an outstanding research book that makes a seminal contribution to the research literature, reflects the highest standards of research exposition, and promises to have a deep and long-term impact in its area." The prize was awarded Jan. 6 in Atlanta, Ga.

The prize honors Thurston's book Three-dimensional Geometry and Topology, edited by Silvio Levy. The book describes Thurston's "geometrization program," a major event in modern mathematics that has the celebrated Poincaré Conjecture as a corollary.

"This is exciting and vital mathematics," the prize citation says. "Thurston's book is nearly unique in the intuitive grasp of subtle geometric ideas that it provides. It has been enormously influential, both for graduate students and seasoned researchers alike. Certainly the army of people who are working on the geometrization program regard this book as 'the touchstone' for their work. A book that has played such an important and dynamic role in modern mathematics is eminently deserving of the AMS Book Prize."

Thurston, who joined the Cornell faculty in 2003 from the University of California-Davis, was the recipient, in 1982, of the Fields Medal, one of the highest honors a mathematician can receive, for his work on manifolds, a generalization of surfaces.

Thurston's Geometrization Conjecture has revolutionized manifold theory, in the process reviving hyperbolic geometry. Before Thurston, scientists thought that hyperbolic manifolds were extremely unusual; he showed that a very large class of hyperbolic manifolds has natural perfect shapes. Being "perfect" means the shape has constant curvature. Thurston's work has linked many apparently disparate fields to manifolds.

Thurston received his bachelor's degree in 1967 at New College in Sarasota, Fla. and his doctorate in 1972 at the University of California-Berkeley. He has taught at the Institute for

Advanced Study in Princeton, N.J., the Massachusetts Institute of Technology, Princeton University, UC-Berkeley and UC-Davis.