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I have a not enough checked for errors proof of an important math conjecture, P=NP (for your calmness: the proof is not very constructive). 8 pages.

Where can I post it for scrutinized checking?

I posted it and the question to check the proof in ResearchGate.net. I tried to post it at PhysicsForums.com but my question was deleted. I posted it on Reddit, with no useful responses. Where else?

I also negotiated to check it for $100 at Fiverr. It's not very small sum and I doubt whether to spend it.

I can't post on arXiv, because I am not affiliated with an institute.

I do realize that the final destination is a peer-reviewed journal. But I want feedback before I submit it to a journal.

porton
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    Sorry for being nitpicky on language matters, but there is no such thing as a "not enough checked for errors proof". Something either is a proof or it isn't. If you don't know whether it contains errors, you don't know whether it is a proof. – Jochen Glueck Aug 18 '23 at 14:39
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    For the specific case of proposed P=NP proofs, you could compare your proposed proof against this list of common warning signs that a proposed P=NP proof is wrong: https://scottaaronson.blog/?p=458. This is written by an author who wrote a well-received survey paper on the P vs NP problem, which probably provides useful prior literature on the problem: http://www.scottaaronson.com/papers/pnp.pdf – isaacg Aug 18 '23 at 16:53
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    If I may make a musical analogy, what you are doing is in effect saying that your interpretation of Beethoven's piano sonatas will blow Richter's and Brendel's and everyone else's out of the water, but you first need someone to listen to it and confirm that you are actually playing the right notes, because you're not quite sure. Just – no. I don't mean to offend, but there is no chance in hell that you have resolved the P vs. NP problem if you need someone else's assistance to confirm whether or not your 8-page (!) argument is logically sound. (I would understand if it were a 200-page proof.) – Adam Přenosil Aug 18 '23 at 17:51

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The reason you are not getting any answers is that P=NP is right there in crank-land along with proofs against evolution, the 2nd law of thermodynamics, general relativity, etc. Nobody wants to even look at your proof because what you are asking is to be educated in some very basic concepts in computer science (or biology, or physics, etc.)

This is not to discourage you, or to say that outsiders cannot make important contributions. It's that you need to do some homework before expecting others to take you seriously.

Is there a single example of an outsider considered a "crank" publishing a ground-breaking result that was found to be correct (in the last 30 years)?

I believe I have solved a famous open problem. How do I convince people in the field that I am not a crank?

Cheery
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    You’re right but this doesn’t answer the question of where they can get their proof checked. – user438383 Aug 18 '23 at 10:41
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    @cheery, there are other "crank-land" red flags too. I looked at the OP's websites and found this link "My projects are more important than yours. Donate all your money (or at least how much you are willing to donate) to me." and another page of his has the popup "A biblical prophecy says that I have the right for 1% of your income (or 10% if you receive tithes)" – Richard Erickson Aug 18 '23 at 13:38
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    https://endofgospel.wordpress.com/2017/04/01/how-much-to-donate/ for the first quote – Richard Erickson Aug 18 '23 at 13:39
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    @user438383 - sure, the first sentence could say ‘There is no chance a competent person will review your paper.’ That is strongly implied from the rest. – Jon Custer Aug 18 '23 at 13:41
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    @JonCuster right but this isn’t really about the OP and whether they are cranks or not. SE is meant to be a repository of useful questions and answers, not a personalised help desk. The actual question OP asked, ‘is there somewhere where someone can reviews a maths paper’ is useful, even if the answer is might ‘no people don’t generally won’t do that’. Dissecting whether or not the OP is a crank isn’t really useful to anyone. – user438383 Aug 18 '23 at 14:13
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    I disagree that this is equivalent to arguments against evolution, thermodynamics, or general relativity. P vs NP is unresolved. It is possible that someone will eventually resolve it. This is in contrast to the scientific theories mentioned, which are pretty settled by now. Resolving P vs NP would be more like resolving Riemann, or completely describing the nature of dark matter. The rest of your post is spot-on. – Xander Henderson Aug 18 '23 at 18:08
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    @XanderHenderson It's not an argument about the nature of the problems, but about the nature of cranks. Please. And the crank is strong on this one. – Cheery Aug 18 '23 at 18:12
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    @Cheery I'm not sure what the "Please" at the end of your comment is supposed to indicate, but it feels rather sarcastic and rude. My point is that cranks often rules-lawyer. You gave examples that are not alike to P vs NP. I offered other examples which might be more alike. I think that those examples, instead, make your point stronger. You are free to take it or leave it. There is not need to be sarcastic in response. – Xander Henderson Aug 18 '23 at 18:15
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In theory, there is a way to get your proof fully verified without the cooperation of other people, namely formal verification. That would involve first formalizing the statement that P=NP, and then proving that statement to the satisfaction of a proof verifier (Lean, maybe?).

Formalizing the statement is in itself not going to be easy but I would expect someone willing to learn a suitable formal system who is very persistent about it to eventually succeed; the project could be made fairly concrete by saying e.g. that Levin's universal algorithm halts in polynomial time on SAT. I think once that is done, someone who has a short correct proof would also eventually succeed in formalizing that, albeit not without significant additional work.

It is however probable that finding a flaw in your proof is far easier. One approach for doing so automatically could be to show your proof to a system like GPT-4 and asking it to highlight the least plausible bit of the argument. While it would certainly not be able to verify the proof, it might just succeed in spotting a part of the argument that is in contradiction to established knowledge or intuitions, and if so, such feedback might be easy for you to verify.

Polytropos
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  • To be honest, I tried to study several proof assistants (at the later stage, Lean) several times. It appears very hard to write proof tactics and I had no more succeess than proving one novel theorem about formal verification. (On the other hand, I am the world-best general topology researcher (there I checked the proofs), this makes for myself plausible that I solve P/NP, even despite I have a trouble write tactics in proof verifiers.) Also my P=NP proof is not easy one: It requires to model ZFC in NBG, what involves many axioms (and theorems). – porton Aug 18 '23 at 21:47
  • I meant not easy one to fully verify formally, without referring to existing results in literature as to axioms. – porton Aug 18 '23 at 21:48
  • GPT-4: "As an AI language model, I am unable to provide a thorough evaluation of your proof since it requires detailed analysis of mathematical concepts and technical details." and further it follows trivial general advice on proof checking. – porton Aug 18 '23 at 21:53