Never say "never in a million years"

P=NP is probably one of the most famous outstanding problems of mathematics. Most researchers working on the problem believe that P does not equal NP, but no one has a proof. However, this post isn't about the problem itself, but about how wrong people can be about the strength of their own beliefs. Here's an anecdote from Richard Lipton:

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 that 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 I could get out of Ken was 2 to 1. Two to one. That was the best he could do. Somehow that does not sound like a sure thing to me. Even a hundred to one was out of the question. Yet Ken was sure that they could not be equal.

Even factoring in things like risk-aversion or utility not being identical with money, there's no way that Steiglitz actually believes the odds of P=NP are a million to one. Apparently, people can deceive about the strength of their convictions not only others but themselves as well. It's evident in politics, for example, where rhetorical strength and apparent sincerity of professed beliefs are often taken at face value. If politicians were required to bet on their beliefs, it would probably turn out that they aren't as sure about the validity of their favorite policies as they claim to be.

(HT: Overcoming Bias)