> Anyway, despite the fact that error-correction is really hard, publishing actually false results was quite rare because "people's intuition about what's true

> Anyway, despite the fact that error-correction is really hard, publishing actually false results was quite rare because "people's intuition about what's true is mysteriously really good." I don't find that mysterious. One aspect of number theory is that results have arbitrarily deep implications and relations. If you are wrong about something you can often substitute it in somewhere else and produce a wrong answer or a contradiction. Doing something wrong which still looks right after being tested from a few different perspectives is extremely tricky. Like finding a pseudoprime for some probabilistic primaility test-- it's not likely to also be a pseudoprime for an unrelated test. So pretty much the only way to pass a collection of independent probabilistic tests is to actually be prime. (Note the 'pretty much'-- a bunch of approximate proofs isn't a necessarily proof, but it at least explains why false things are seldom believed even when their headline proofs aren't solid) I don't just mean through different reviewers -- when you publish a proof of something you've probably satisfied yourself that it was true through multiple avenues. The proof you published was just the one you thought was the most convincing. Unfortunately, making an error in it can be something that makes a proof more convincing (until the error is found), but fortunately having an incorrect proof of something doesn't make the underlying fact untrue.