I'd hazard to argue that this is the most ridiculous "sketch" of a mathematical proof I've ever seen:
The proof is then rather simple and here's a sketch: take a non-linear sigma model (string theory) on your simply-connected three-manifold, and flow it to the infrared. The manifold can be seen to become increasingly smooth and the only possible endpoint is the three-sphere.
But my problem is more that Lubos tries to argue that this wonderful work (largely due to Hamilton and Perelman) is somehow part of string theory!
(in his comments, someone "predicts" that Lubos' critics will find a way to bash this post!)