[1] William Thurston suffered from congenital strabismus as a child, causing issues with depth perception.

[3] Following this, he received a doctorate in mathematics from the University of California, Berkeley under Morris Hirsch, with his thesis Foliations of Three-Manifolds which are Circle Bundles in 1972.

His more significant results include: In fact, Thurston resolved so many outstanding problems in foliation theory in such a short period of time that it led to an exodus from the field, where advisors counselled students against going into foliation theory,[9] because Thurston was "cleaning out the subject" (see "On Proof and Progress in Mathematics", especially section 6[10]).

His later work, starting around the mid-1970s, revealed that hyperbolic geometry played a far more important role in the general theory of 3-manifolds than was previously realised.

Inspired by their work, Thurston took a different, more explicit means of exhibiting the hyperbolic structure of the figure-eight knot complement.

Together with his analysis of deformations of hyperbolic structures, he concluded that all but 10 Dehn surgeries on the figure-eight knot resulted in irreducible, non-Haken non-Seifert-fibered 3-manifolds.

The proof involves a number of deep and original insights which have linked many apparently disparate fields to 3-manifolds.

[13][14] In his work on hyperbolic Dehn surgery, Thurston realized that orbifold structures naturally arose.

[15] Two teams of mathematicians around 2000 finally finished their efforts to write down a complete proof, based mostly on Thurston's lectures given in the early 1980s in Princeton.

[1] Thurston received the Fields Medal in 1982 for "revolutioniz[ing] [the] study of topology in 2 and 3 dimensions, showing interplay between analysis, topology, and geometry" and "contribut[ing] [the] idea that a very large class of closed 3-manifolds carry a hyperbolic structure.

"[16][17] In 2005, Thurston won the first American Mathematical Society Book Prize, for Three-dimensional Geometry and Topology.

[18] He was awarded the 2012 Leroy P. Steele Prize by the American Mathematical Society for seminal contribution to research.