This response strikes me as very well written. If I received a lot of such proposals to read a non-mathematician's attempted proof of some famous theorem, I would respond much as Jim did (had I thought of making the good points he makes). Personally, I don't receive many such proposals (maybe never) — and so I might ask the amateur to send me a brief sketch of the main points in the proof before declining to read it, just in case it has something of value. I confess I still feel there must be some proof of FLT that's much more elementary than Wiles / Taylor (which goes far beyond the math that I can understand at this point). —Dan
On Jul 2, 2015, at 11:57 AM, James Propp <jamespropp@gmail.com> wrote:
Recently someone wrote to me saying (apropos of FLT)
About a year ago an idea presented itself to me such that I know it is
correct. I can "prove" 90% of it and demonstrate 100% of it. However I am not a mathematician and a formal proof is not something I can accomplish. Would you be willing to examine my paper? At the least, you can use it as a bad example. If it's not laughable, then I'd be happy to ask you to be co-author.
Here's what I wrote to him; comments?
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I hope you'll forgive me if I treat the matter statistically. (Nobody is a mere statistic in his/her own eyes, but in the eyes of other people, we all inevitably are.) Nearly all attempts at proofs of FLT by mathematicians and non-mathematicians alike over the past few centuries have failed. The difference is that the mathematicians' failures have sometimes (not often, but sometimes) been educational: the flawed argument covered important infinite classes of possible counterexamples and ruled them out, or the flaws in the proof, when brought to light, uncovered important facts about whole numbers. Amateurs' failures, in contrast, when brought to light, uncovered facts that are well-known to number theorists, so the only ones who benefited from the bringing-to-light were the amateurs themselves, not the mathematical community at large, and not the bringer-to-light (typically a sympathetic mathematician or a graduate student who was given the proof by the more senior mathematician to whom it had been sent, as a way of helping the graduate student sharpen his/her skills).
None of which rules out the possibility that you are the rare exception: an amateur with an approach that is both new and valid. In fact, I would say that, given what I know about you, the chance of that unlikely event is not one in a billion (the probability I'd assign if you were just a random mathematical amateur) but one in a million, since you've already shown an ability to come up with new and valid ideas in another field.
Still, my time is finite, like my money, and I don't play the lottery with my money, so I don't want to invest a lot of time into a project that, from my point of view, is unlikely to lead to anything.
But: you've been generous with me, so I'm willing to spend an hour taking a look at what you've done and giving you my feedback.
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It occurs to me that there might be some way to be pseudo-quantitative and do a cost-benefit calculation to quantify just how much time I should spend reading his draft of a proof of FLT.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun