William Thurston died yesterday of cancer, aged 65.

Thurston was one of the greatest contemporary mathematicians; a huge figure in low-dimensional topology. I won’t bother writing out a mathematical biography – Wikipedia and MacTutor have all the relevant information, as usual, and I won’t pretend I know a huge amount about the exact details of Thurston’s achievement. Instead, I’ve tried to gather together a few links from around the web that give an idea of why Prof Thurston was so widely admired.

Thurston’s great work was to formalise the maths of three-dimensional spaces, an effort which produced the book *Three-Dimensional Geometry and Topology: Volume 1*, an expansion of lecture notes produced in the 80s which became an instant classic for its quality and scope. In 2005 the book won the first AMS Book Prize. The prize “recognizes an outstanding research book that makes a seminal contribution to the research literature”. If you can’t get hold of the book, a newly typed-up version of the original notes is online at the MSRI.

In 1982 Thurston proposed his geometrization conjecture, which states that “compact 3-manifolds can be decomposed canonically into submanifolds that have geometric structures”. It turned out that the geometrization conjecture had the Poincaré conjecture as a corollary; it was Thurston’s statement that Grigori Perelman finally proved in 2003.

It seems Thurston was quite active on MathOverflow; his profile page is quite interesting.

In 2010, Thurston collaborated with Dai Fujiwara on a line of clothing inspired by his geometric models. You can see the two discussing the work here:

A document that has been circulating along with news of Thurston’s death is his essay “On proof and progress in mathematics“, in which he discussed with great insight some of the big questions about the culture of mathematics: what is it mathematicians accomplish; how is mathematical understanding communicated; what is a proof?

Finally, here’s a video of a lecture delivered by Thurston in 2010, titled “The Mystery of 3-Manifolds”, found via Andrew Greene.

Daina Taimina has written a blog post in memory of her friend and colleague: http://hyperbolic-crochet.blogspot.co.uk/2012/08/bill-thurston-1946-2012.html.

Someone at Cornell’s maths department has put up a page collecting memorials: http://www.math.cornell.edu/spb/comments.php?y=12&m=08&entry=entry120822-104909