The Mathematician Who Changed the Shape of Three Dimensions

William Thurston changed modern topology by replacing a fragmented collection of problems with a geometric vision of three-dimensional manifolds. Born in Washington, D.C., in 1946, he graduated from New College in 1967 and earned his Berkeley doctorate in 1972. His work on foliations, hyperbolic manifolds and geometrization created a new language for low-dimensional topology. This documentary follows the ideas that earned the 1982 Fields Medal and later guided Perelman’s proof of the Poincaré conjecture.

Before Thurston, three-manifold topology often appeared as a collection of isolated puzzles. His geometrization conjecture proposed that these spaces decompose into pieces carrying one of eight geometries, turning classification into a coherent program. The vision transformed topology and eventually led to Perelman's celebrated proof. Thurston also changed how mathematicians think about understanding itself, emphasizing pictures, intuition and communication. This documentary reveals a revolution in both mathematics and.