I once had a long discussion with Ken Steiglitz about P=NP, while I was still at Princeton. … Ken was and still is sure that P must not be equal to NP. Okay, I said to Ken, what are the odds that they are equal? Ken said that he thought the odds were a million to one. I immediately suggested a bet. I did not ask him to “bet his life,” but I did ask for a million to one bet. I would put up one dollar. If in say ten years P=NP had not been proved, then he would win my dollar. If P=NP was proved in that time frame, then I would win a million dollars from Ken. Ken said no way. After more discussion the best bet I could get out of Ken was to . Two to one. That was the best he would do.
That is from Richard Lipton; hat tip to Michael Nielsen. Does anyone doubt that two to one better summarizes his evidence than a million to one?
Ian Maxwell, I would be happy to bet my $100 against your $10k that PvNP is shown to be undecidable by Peano arithmetic within the next 20 years. If you cap your losses at $100, it doesn't look to me worth the transaction costs to collect 20 years in the future, so I won't put up my $1. Similarly, I don't think my first offer gives you any upside.
Thanks - great story!
I'll take your bet at, hmm, 20 to 1. Up for it?Anyone else want to post the odds they'd take the bet at?