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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?

Balbanna
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    Really, you proved? – Inquisitive Jan 10 '13 at 15:22
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    Why do you have the tags number theory , calculus – Amr Jan 10 '13 at 15:24
  • The proof attempt is in number theory with some calculus in the logic. – Balbanna Jan 10 '13 at 15:26
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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
  • @Amr: that I got :) (as a respond to your comment to your answer). You're not alone - at least 5 other people wonder which conjecture is meant, so let's hope OP tells it. – Ilya Jan 10 '13 at 15:50
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    The fact that the problem you think you solved is number theory and calculus is irrelevant to this particular question, since you are not asking about the problem. I've removed those tags. – Thomas Andrews Jan 10 '13 at 15:55
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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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    @Carl, surely you are a little bit curious? You _are_ human, aren't you? – TonyK Jan 10 '13 at 16:18
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    Well it will be exciting if he's proved the Riemann Hypothesis but Goldbach's Conjecture ... not so much. I eagerly await this mathematical breakthrough. – TheMathemagician Jan 10 '13 at 17:02
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    He or she. $ $ $ $ – Did Jan 10 '13 at 17:13
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    OP seems to be a nice choice – Ilya Jan 10 '13 at 17:31
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    R.H. proved by a non-mathematician would be as likely as having aliens landing on Washington or Moscow and asking for the next gas station on this side of Jupiter...but *even* from failed attempts (e.g., Lamé with FLT) one can learn a lot. – DonAntonio Jan 10 '13 at 17:38
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    @Amr: at least you can make a conjecture, what the original conjecture is. – Ilya Jan 10 '13 at 17:44
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    I'm not active there, but wouldn't "Is $P$ a valid proof of the conjecture?" be a valid question on MathOverflow? – AakashM Jan 11 '13 at 09:05
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    @DonAntonio What constitutes a mathematician? A Paper certifying that you've been through certain courses or a an understanding? – Balbanna Jan 11 '13 at 20:59
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    @Balbanna, I'd say someone knowing the basic stuff as usually taught in undergraduate schools in most western countries (this is *my* own personal definition), so that (s)he has the basic tools to at least understand the basic terms and notions in the R.H., say. Please do note I wrote "knowing", not "having a diploma, title or whatever". – DonAntonio Jan 11 '13 at 21:02
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    @DonAntonio: So what you are saying is that somebody who doesn't understand the statement of the Riemann Hypothesis is unlikely to come up with a valid proof of the Riemann Hypothesis. I'll go along with that... – TonyK Jan 11 '13 at 21:22
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    @AakashM: No, MathOverflow usually quickly closes questions of the form "Please check my proof of ...". – Andreas Blass Jan 11 '13 at 21:32
  • Exactly, @TonyK. That's one ot the reasons almost no crank/troll/ignoramus messes with R.H.: one needs some basic education in university mathematics to understand it, unlike what happens with Cantor's theorem or Fermat's Last Theorem, which can be understood by any decently educated high school student...and thus they attract more cranks. – DonAntonio Jan 11 '13 at 21:34
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    I recommend you read [How to Write a Proof](https://www.dropbox.com/s/lu7at0u6inuy1cu/How%20to%20write%20a%20proof.pdf) by Leslie Lamport. The proof style described there (structured proofs) have been tested by the author to prove some results in CS. I don't recommend you send a paper full of structured proofs (it depends of the result) but I recommend you understand how it works and then try to adapt the proof of your result to an structured proof. I your argument is wrong, it will be immediately obvious. – leo Jan 16 '13 at 15:20
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    You could also pull a Perelman and just post it one Arxiv – JohnPhteven Jan 23 '13 at 11:17

8 Answers8

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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.

TonyK
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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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    True that, I only pointed it out in case OP has such opportunity - that just may be safe. As OP said, he is a CS student which with a high probability means that he has a right to post on arXiv (at least, with probability higher than the one that there are no mistakes). – Ilya Jan 10 '13 at 15:34
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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
  • @Carl: You may be right. Or perhaps the OP would rather be judged by strangers. – TonyK Jan 10 '13 at 16:03
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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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    @Thomas Andrews: paranoia and conspiracy theories aside, I believe contacting a trusted colleague or, in this case, a mathematics professor whom the OP already knows is the best way to get feedback about such things. – Carl Mummert Jan 10 '13 at 16:15
  • A nice compromise might be finding computer scientist, who sometimes publishes in math. There are a few. So, hopefully the computer science researcher will be able to communicate with the OP, while at the same time having some idea of what mathematicians are looking for. – Henry B. Jan 10 '13 at 16:21
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    I believe that we should not underestimate the question (and nor encourage it). Remember the AKS primality test done by students of computer science in India. The AKS primality criterion surprised the world in 2002. And left the community . constrained by mathematical simplicity. See AKS test in http://en.wikipedia.org/wiki/AKS_primality_test – Elias Costa Jan 10 '13 at 18:28
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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
  • You think you have made some major contribution to answering this stack exchange post. You are most certainly mistake. -1 – Abstract Space Crack Oct 15 '16 at 15:30
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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.

Henry B.
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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.

Update [01/19/2017] Be careful to avoid journals classified as potentially predatory.

Elias Costa
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  • The newly linked list (which is no longer updated for currently unknown reasons) is not that useful for math. A very simple rule will allow one to avoid everything on that list anyway: Do not pay to publish your math paper but instead put it on the arXiv as the OA option. – Tobias Kildetoft Jan 19 '17 at 15:55
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I would suggest consulting with one of your mathematics professors at your university.

CramerTV
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  • what if that professor would steal the proof? – Vicrobot Jul 12 '19 at 07:03
  • @Vicrobot, That sounds like a great question to ask the site. – CramerTV Jul 12 '19 at 17:59
  • actually I've got very simple & elementary proof for Fermat's last theorem. Can i post that proof directly here on this site like as said in TonyK's answer? https://math.stackexchange.com/a/275197/547918 – Vicrobot Jul 12 '19 at 18:23
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    @Vicrobot, it looks like there is a tag for that - proof-verification. Click the following link and then post your proof. Good luck! https://math.stackexchange.com/questions/tagged/proof-verification – CramerTV Jul 12 '19 at 22:55
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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.

Lucas Wiman
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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.

RSh
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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.

anon
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The only known way to learn to write proofs up to the mathematical community's standards is: experience.

GEdgar
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