Just a quick note here to say how sad I was to hear (via Terry Tao’s blog) of the death yesterday of Bill Thurston, whose work, particularly on 3-manifolds, endeared him to mathematicians and physicists and resulted in the 1982 Fields medal. I’m certainly no expert on his work, but I encountered it first thirteen years or so ago when I was working on the idea that compact hyperbolic manifolds might provide interesting examples of the extra dimensional spaces used in large extra dimension models.
I found the whole area to be fascinating, and it was particularly interesting for a non-expert because the GeomView program, produced by the Geometry Center (which Thurston had been involved with, and which had just closed) allowed great visualizations of complicated manifolds. They also produced wonderful videos, like this one (that Tao also links to) of Thurston’s method for everting the sphere.
I never met Thurston, but greatly enjoyed the small part of his work that I’ve used, and am very sorry he won’t be around to contribute more.