dasimov@earthlink.net wrote:
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.)
I'm sure it has. This reminds me of a discussion of proofs in the book "What is mathematics, really" by Reuben Hersch. If I remember correctly, he talks about how over time, important proofs come to be accepted as correct, as people in the field examine them. It's a social thing. Did people accept the proof of the 4-colour conjecture when it came out in 1976? Do people believe it more now than in 1976? Probably yes, because it has been gone over and redone by people in the field. Hales' proof of the Kepler conjecture was published while at the same time it has not been 100% fully checked, according to this: http://www.newscientist.com/channel/fundamentals/dn8743.html In the end, it's down to the experts in the field to decide. For a long proof, it takes time. It took a while for Wiles' proof to be examined and accepted. For Perelman's proof, eventually the people in that field will come to a consensus, and the rest of us just believe them. It's interesting right now, we are in the middle of the procedure. Not everyone is convinced: http://www.theaustralian.news.com.au/common/story_page/0,5744,18204052%255E3... Gary McGuire