Thales Posted September 1, 2004 Share Posted September 1, 2004 There has been much talk of late of a Russian mathematician(Dr. Perelman) 'proving' the Poincare conjecture. For those of you who don't know it and are curious check google, as it is a one of the biggest problem in maths, that has been round for 100 years or so, and will take much too long to explain in detail here. For those of you who are familiar with it and the supposed proof adopted using Ricci flow and 'snipping' the singularities, does it appear to you to be more of a quick fix approach than a rigorous mathematical proof. For instance at what point does one decide where to clip the singularities? Is it an arbitrarily defined point? Isn't the inclusion of discluding regions of a 3-mainfold contrary to the principles of topology. For instance the homotopy of a dumbell (used in the popular proof) is distinctly different from the two 3-spheres created from 'snipping' the singularities generated by Ricci-flow out of the equation. As I am not a mathematician myself, proving my skepticism would probably take longer than it is worth, but it is my prediction that the conjecture remains unproven, at least via first principles. The method outlined is an approximation. Link to comment Share on other sites More sharing options...

matt grime Posted September 1, 2004 Share Posted September 1, 2004 I don't think you've grasped some of the complexity of the proof that perelman's put forward, and I think you'd need to explain what you think "snipping" means. There are many ways to smooth out singularities, such as crepant resolutions, I don't know which perelman uses, but they are not at all disquieting. Lots of people think that perelman's proof is correct in spirit, though they can't follow the details, and with more complex proofs necessarily being required more frequently that is something w might have to get used to. Look at Wiles's proof of FLT, actually he proved the semi-stable T-S conjecture, and got that wrong to begin with, and with the help of others corrected his proof and gave a lead for proving the general case. That is perhaps what we will find with perelman, that there may be some cases he's not considered fully, but that a group effort will eradicate them. I don't understand what a dumbell has to do with anything. Link to comment Share on other sites More sharing options...

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