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True, but even then, how large do you think the field is? And how many people verify these proofs? I have a PhD in an esoteric field myself. There's literally
by Moodles 8y ago
True, but even then, how large do you think the field is? And how many people verify these proofs?
I have a PhD in an esoteric field myself. There's literally <50 people worldwide who write/verify proofs in it. I've spotted errors in my own work or other's work that got past peer review. And I don't think I'm particularly special. There's just not enough eyeballs, time and incentives sometimes.
- bsder 8y ago> True, but even then, how large do you think the field is? And how many people verify these proofs? It only takes one to break it. And, for something so fundamental, it's a big deal if you are the one. This isn't physics, where you have to rule out all manner of confounding data before you can trust your conclusion.
- fjsolwmv 8y agoThe point you are missing that studying a proof can't proof it correct, only fail to disprove it.
- bsder 8y agoThat's incorrect. For example, given the axioms of Euclidean geometry, I can prove that the sum of the angles of a triangle add up to 180 degrees. That statement is true. Full stop. Now the starting axioms may not be correct (the parallel postulate, for example, is not required to be true). However, given the starting axioms, proofs are true. Period. In addition, there will be things in mathematics that you cannot prove--Godel's Incompleteness Theorem sits in this section. And, science has the problem that a hypothesis can only be disproven. Mathematics does not suffer from the same issue, though.