Sadly, Bill Thurston passed away yesterday. He was famous for his contributions in many areas of topology and geometry. Not least of which was his Geometrization Conjecture (which was key to the proof of the famous Poincaré conjecture). We also know of Dr. Thurston as a fashion icon.
He’ll be missed.
To read more about Dr. Thurston’s work, check out Terry Tao’s post about his work. In particular, read about Dr. Thurston’s proof of Smale’s result commonly called Smale’s Paradox: a sphere can be turned inside out in three dimensions without causing creases, pinched points or any other nondifferential points as long as you allow self-intersections. Amazingly, the 2-D version (turning the circle inside out in the plane) is not possible!
Here is a cool video by the defunct U of MN Geometry Center explaining the eversion of the sphere: