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On a related note, Scott Aaronson once wrote up a few heuristics he uses to quickly evaluate how likely a P/NP proof is to be incorrect: https://www.scottaarons
by throwawaymath 7y ago
On a related note, Scott Aaronson once wrote up a few heuristics he uses to quickly evaluate how likely a P/NP proof is to be incorrect: https://www.scottaaronson.com/blog/?p=458 https://www.scottaaronson.com/blog/?p=458
Aaronson’s rules are more technical than the ones given in this article, the latter of which can be generally applied to most claimed (dis)proofs of famous open problems. In particular, poorly typeset papers from a solo, unknown authors are highly unlikely to be correct when they’re claiming to resolve well known open problems.
In regard to the P/NP problem specifically, Aaronson’s examples of weaker open problems which would likely be resolved first - or at least accounted for in some nontrivial way - are analogous to this article’s point about proving weaker theorems first. It would be very suspicious for a proof that P and NP are separable (or not separable) to work at such a high level that it doesn’t prove also new results about the lower bounds of a litany of other problems.
- mormegil 7y agoI thought you meant a simpler heuristic http://haspvsnpbeensolved.com/ http://haspvsnpbeensolved.com/ :-)(I had thought Scott Aaronson is somehow connected with it, but probably not, it seems)
- btrettel 7y agoI know the guy who made that website. I think it might have been done at the request of Scott, or Scott advertised it on his blog at some point.
- pmiller2 7y agoThat’s kinda funny, but it should at least throw an error when you click the button without providing a URL. :P
- verma7 7y agoI hope to see the day when this website gives the wrong answer.
- neilv 7y agoIs all the good math institutionalized now (e.g., you can't do good math without all the benefit of learning background within the institution conventions)? What's the intuition that an extremely important proof will come from someone who gets all the TeX tweaked to camera-ready perfection, goes around and gives the talks, and all the conventional things... rather than a genius out of nowhere who walks into a stranger's office, wordlessly drops on their desk a stack of handwritten pages wrapped in twine, and walks out, never to be seen again? I was thinking of this because I once knew an autistic person, from some humble and isolated upbringing, who was getting some informal math instruction, and they told me they thought they knew a proof for P=NP. I considered it extremely unlikely, but not utterly impossible. (They reportedly tested "off the scale" high in some particular cognitive regard, and I'd noticed a couple minor superpowers.) If that person, to use them as an example, ever actually worked out the proof, and wanted to "turn it in" with their own judgment and access, I wonder where they'd go. And whether it would be somewhere that would take them seriously enough to look at it, and whether they could tell that a proof in unconventional terms had merit. If they get turned away from the first place, would they be discouraged and give up, or would they keep trying, there or elsewhere. If they persisted, would they appear to be a crank because of their persistence and frustration.
- azernik 7y agoI think the intuition is that the best mathematicians, autistic or not, tend to be in academia already. So your prior for someone from the general population should be that they're more likely to be a crank than a genius, ie non-academia has many more cranks than geniuses.
- neilv 7y agoIt's definitely intuitive to me that most all claims from outside the institution will be mistaken/naive. But, for really big wins that have thus far evaded the institution, what's the likelihood that the solution will come from within the institution rather than from outside? (I'm asking sincerely; I'm not a mathematician, and don't know.)