Does that mean geometry is going to have some sort of renaissance?
DH: Oh yes, geometry is having a renaissance. One indication of this is the number of geometry courses being taught around the country. For example, when I first came to Cornell there was only one undergraduate geometry course; now we have eight. A further indication is the work of William Thurston, who has hypothesized a classification for the different types of three-dimensional manifolds —the three-dimensional analogues of two-dimensional surfaces (such as the surface of a sphere or a donut). Where two-dimensional geometry comes in just three types—the Euclidean plane, the sphere, and the hyperbolic plane—Thurston’s Hypothesis says that there are eight distinct 3-D spatial types. Over the past year the mathematical world has been excited by the news that Thurston’s Hypothesis might have been proved. If that turns out to be true, then mathematics most famous geometric problem – the Poincaré Conjecture—will also have been proved, and there’s a million dollar prize attached to that dis
