How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical community's standards? [closed]

Solution 1:

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.

Solution 2:

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.

Solution 3:

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:

• http://mathworld.wolfram.com/UnsolvedProblems.html

• http://www.openproblems.net/

• http://www.openquestions.com/oq-math.htm

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

• http://www.jstor.org/action/showAdvancedSearch

• http://www.ams.org/mathscinet/msc/msc2010.html

• http://arxiv.org/multi?group=grp_math&%2Ffind=Search

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

• http://www.scimagojr.com/journalrank.php?area=2600&category=0&country=all&year=2011&order=sjr&min=0&min_type=cd

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.

Solution 4:

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

Solution 5:

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.