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I'm a computer science student who is a maths hobbyist. I'm convinced that I've proven a major conjecture. The problem lies in that I've never published anything before and am not a mathematician by profession. Knowing full well that my proof may be fallacious, erroneous, or simply lacking mathematical formality, what advice would you give me?

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I don't know if this is a good idea. Why don't you discuss your work with a mathematician whom you trust. –  Amr Jan 10 '13 at 15:27
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May I know what the conjecture is ? –  Amr Jan 10 '13 at 15:27
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@Amr: I don't see that it makes much difference what the conjecture is. –  Carl Mummert Jan 10 '13 at 15:57
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Have you informed yourself about other peoples attempts to show the conjecture? Chances are, You may even find your method as a failed attempt ... (again, this is not to discourage you) –  Hagen von Eitzen Jan 10 '13 at 16:01
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He or she. $ $ $ $ –  Did Jan 10 '13 at 17:13

7 Answers 7

I'm convinced that I've proved a major conjecture.

You are almost certainly mistaken. I say this on purely probabilistic grounds, so don't get upset $-$ even professional mathematicians are sometimes mistaken about their own 'proofs', and amateurs almost always.

I suggest you tell us what this major conjecture is, and post a link to your proof (or just post it here, if it's short enough). This is enough to establish your priority, if you are worried about somebody stealing your proof. Then the sharks of MSE can devour it.

PS Your proof will probably be more favourably received if it is nicely formatted, using LaTeX.

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I am not sure, but maybe arXiv works better as a source to establish the priority? –  Ilya Jan 10 '13 at 15:30
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@Ilya, that would certainly be true, if arXiv was open to all. Perhaps the OP has posting rights, perhaps not. –  TonyK Jan 10 '13 at 15:32
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I don't think it's necessary to tell us what the conjecture is, or post a link. I would suggest that the OP find a math professor at his or her home institution and ask them in confidence. It's always better to have someone else look at anything "major" before posting it on the internet. –  Carl Mummert Jan 10 '13 at 15:59
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If it is a valid proof, though, a single mathematician might well steal it, while a public posting makes it much more difficult for someone else to falsely claim authorship. @CarlMummert –  Thomas Andrews Jan 10 '13 at 16:07
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If your concern is establishing priority you should make it public as quickly as possible; if your concern is avoiding embarrassment you should have it reviewed in private. But if you trust the reviewer there shouldn't be much of an issue either way. –  Charles Jan 10 '13 at 18:32

Many graduate students and people who try to switch fields often face this problem. Although, they might have a cool idea, they just don't have the knowledge about the right way to present the idea. Also, because they don't know the field very well, from the perspective of the field's community, their work is a weird mix of well-known results, irrelevant details and unexpected points-of-view. In the middle somewhere, there might be a brilliant idea. Quite often, reviewers will not have the patience to look for that cool idea. The less well you know the field, the more painful the review process will be for you and the review process is already painful enough for most.

Even researchers who are well-established can have this problem of not knowing how to express their idea for an unfamiliar field.

I would advise doing a lot of reading in the field that you think your proof belongs to until you can speak their language reasonably well. It's not unusual for this to take months. Most graduate students have to do this. A second approach would be to collaborate with somebody who is already established in your target field. In my experience, this is a common strategy for established researchers.

Don't be surprised if you spend longer figuring out how to write up and present your idea, than it took to do the actual research. That's pretty common!

I wouldn't go public as there is a lot of potential for embarrassment there and well, reputation does matter ... for instance, in cases where you are trying to get a collaborator.

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Update: I think that the post 'Be sceptical of your own work' by Terence Tao (winner of the Fields Medal in 2006) can help you with your answer. See too Don’t prematurely obsess on a single “big problem” or “big theory”. In his blog 'What's new' Terence updates on research and expository papers, discussion of open problems, and other maths-related topics.

If the conjecture is important it has a name and keywords associated with it.

Step 1: Primary search. First you should do a literature search (using the 'name of the conjecture' and 'keywords') on your conjecture. Visit pages from reputable mathematical websites that discuss open conjectures. And see if your conjecture is still open. Eg:

Step 2: Fundamental search. Go to respectable databases with subject classifications:

Then use the 'name of conjecture', the 'keywords' and an appropriate classification for searches in databases. And see in the articles you find if this conjecture is not resolved or what contributions were made. See if there is a program to solve it. (As was the case with the BMV Conjecture, now resolved (?).) If your proof is in the direction of a program you did not know then your evidence may be right.

Step 3. Submit If after doing all of this you still believe that your proof is correct, write an article, look at a journal in scimago database

that is compatible with the field of mathematics to which the conjecture belongs. Enter the journal page and follow the procedures for submitting articles.

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At step 3, I presume you mean a "journal" not a "newspaper". I know the New York Times would be very confused if they received a mathematical proof :P –  drxzcl Jan 10 '13 at 19:03

I would suggest consulting with one of your mathematics professors at your university.

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At the very least, you would need to avoid the pitfalls found in Scott Aaronson's Ten Signs a Claimed Mathematical Breakthrough is Wrong.

I tend to agree that it's incredibly unlikely that you have in fact solved a major conjecture. At various times as an undergraduate, I was convinced of solving major and minor conjectures. It's really very easy to fool yourself.

I'd say email a math professor at your university in the relevant specialty, and ask to meet with him/her for an hour or so to go over what you've been working on. They'll probably be able to quickly spot a major flaw in your work, and if not, they'll be extremely interested in working with you. If you approach them with the right humility about the correctness of your proof, most profs would be thrilled to interact with a student who is actually interested in research. You might talk about doing an REU or something similar in the general area of the conjecture if things go well.

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There is no Explicit answer to your request. but first of all you should determine the field of mathematics which agrees with your research.

The second step is to read some texts about your work esp. papers published.(I guess you solved the conjecture by reading related mathematical papers or books! isn't it?!)

And as a final step you may write down a simple and related proof from a paper which you understand it.

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While, as mentioned by many others, the best answer is definitely to consult with a trusted mentor, here's one thing you should have already done; you need to go over your proof with a fine tooth comb, and be extremely critical as you do so. You need to make sure that you are able to provide an air-tight proof for every single assertion on every page, and anticipate possible objections. This is tedious, difficult work, possibly harder than coming up with the idea of your proof in the first place, but also is absolutely necessary, moreso as you are claiming to prove a major conjecture.

Of course, your final published version will probably not contain this level of detail, and this process doesn't guarantee that mistakes won't get through (even for the world's best mathematicians) but you should be much more confident that your proof is not "erroneous or fallacious", as you put it in the OP, before claiming to have settled a major conjecture.

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