Apropos proof-checking by any means: In Fall, 2002, the Russian mathematician Grigori Perelman posted to the math ArXiv website some papers claiming to prove W. Thurston's geometrization conjecture (TGC) <http://en.wikipedia.org/wiki/Geometrization_conjecture>. If true, TGC would greatly advance the field of 3-manifolds, and would also imply the famous so-called Poincare conjecture (PC) as well (one of the seven Clay $10^6 prize problems). Since then Perelman has given detailed lecture series at a number of U.S. math departments, and undoubtedly many others around the world. Ever so slowly, the experts in this field seem to be concluding cautiously that at least the part of Perelman's work that purports to prove the PC is *probably true. They're less sure about the entire TGC. (I believe there is at least one piece of the TGC proof that Perelman has promised to post on the ArXiv, but has not yet done so.) In March, 2004, Scientific American published an article that stated that PC had been proved by Perelman. Everyone I asked who attended any of his lectures expressed cautious optimism for PC, but none would affirm that it had been proven. That October, John Morgan of Columbia published an article written in August, 2004 that discussed Perelman's work, but he dd not affirm that the proof was correct. Though the optimism is slowly increasing for PC, it still seems no one among the experts is ready to publicly affirm that PC has been proven. For me this is a bit like watching a drama of high suspense unfold in slow motion. Assuming the absence of reliable automated theorem-checkers for this kind of proof, how do we decide when Perelman's work is correct? (Incidentally, he has apparently never submitted it to a peer-reviewed journal, but some sources say it's already gotten much more careful scrutiny than most such submissions would.) --Dan _________________________________ * Poincare didn't actually phrase this as a conjecture; he asked whether or not it was true.