I won’t pretend to know what the Poincaré Conjecture’s about, but I think it has something to do with turning spheres inside out. Whatever the math is, I just think the animations are cool. The Berkeley Science Review interviews Stephen Smale, who did the proof for seven (and later five) dimensions and above. Go to this page for the accompanying video. Here’s another video with some explanation (although the method seems different–does someone know the difference?).
