William Thurston
1946–2012, Washington, D.C., United States, Rochester, New York, United States
GeometryTopologyAlgebraFields Medal 1982
American mathematician who revolutionized the study of three-dimensional manifolds through geometric structures and the geometrization program.
William Thurston developed a vision in which three-dimensional manifolds are assembled from canonical geometric pieces. His geometrization program unified hyperbolic geometry, topology, and group theory and became a foundation for Perelman's later proof of the geometrization and Poincare conjectures. Thurston received the 1982 Fields Medal.
Workplaces: Princeton University, University of California, Berkeley
United States
Award-winning work
Fields Medal 1982The 1982 Fields Medal honored Thurston's transformation of low-dimensional topology. His geometrization conjecture proposed that every compact 3-manifold decomposes into pieces each carrying one of eight canonical geometric structures, and he proved the hyperbolic part for Haken manifolds — an enormous class — by constructing hyperbolic metrics via pleated surfaces and deformation theory. He also reshaped the theory of foliations, codimension-one in particular, and the classification of surface diffeomorphisms through his work on train tracks and pseudo-Anosov maps. The geometrization framework subsumed the Poincaré conjecture and supplied the program that Perelman completed two decades later.