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!)

## 3 comments:

I think you would make a great decision if you remained silent about things about which you have absolutely no idea.

Of course that Perelman's work is based on mathematics of perturbative string theory, and he refers to it properly. If you read his main paper math/0211159, you will see on page 6 that he uses the standard string theory results that he needs, and he introduces the stringy terminology, too, because the problems he studies are relatively standard in string theory.

Also, the top 2 cited papers (and many others) that refer to Perelman's paper are string theory papers, see here.

Finally, Perelman's work is interesting and valuable for math - and financially about which he rightfully does not care - but you can't compare the beauty of this single work with the beauty of string theory as a whole theory.

Lubos,

First, let me say that my post was meant to be somewhat lighthearted. I can sympathize with your position...afterall I picked the title of my blog "not for nothing."

You assert that

Perelman's work is based on mathematics of perturbative string theory

which I doubt. Even the way Perelman references string theory, he says

The functional [...] can be found in the literature on the string theory

which only says that the two fields (Ricci Flow and string theory) use some of the same mathematics. That string theory papers reference his work is also consistent with this.

I've got no problem with string theory. I think it's had some remarkable progress, and it's interesting. I'm just not ready to tell the LQG folks (or others) to give up with what they're doing. Nor am I willing to give string theory credit for these wonderful results in

Ricci Flow.

Keep on blogging!

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