How do I ensure I'll be able to claim authorship over a math proof, as an amateur math student?

Question

I found proof for an open math problem. I know it likely has flaws, but I can't catch any and I'd like to put the proof out for revision. But without losing the credit for it, in case it turns out to be correct.

The thing is I'm just a math student and I have no experience publishing math papers or anything.

I've already checked a post here with the same question I'm asking, in which many people recommended talking first with a mentor or a trustworthy teacher, but I've never had a relationship with a teacher. And currently, I'm not seeing my teachers in person, because I'm in quarantine and my classes are virtual. Moreover, it would be really embarrassing for me to talk about this with people I know, especially if they rapidly find a mistake in the proof. I fear they'd think I'm silly for even considering the possibility I may have proven something no mathematician has been able to prove before. So I don't want to share this with anyone I know unless the proof is reviewed by expert mathematicians and I'm fully sure it's correct or at least seems to be.

Finally, as you may have noticed, English isn't my native language, so I don't know how I could manage to write down this proof in English. I'm not familiar with the math language and notation used in English.

I want an English version because once the proof is published, I'd like to send it to important mathematicians for revision and I don't know important mathematicians who speak my language.

Answer 1

Moreover, it would be really embarrassing to me to talk about this with people I know, especially if they rapidly find a mistake in the proof. I fear they'd think I'm silly for even considering the possibility I may have proven something no mathematician has been able to prove before

My advice for this concern is to propose your work as an attempt rather than conclusive. It is normal and okay for attempts to fail: most do. If you reduce your expectations publicly to those that you hold privately, there is little cost to failure and substantial benefit to success. Ask others to find errors in your work, and be humble.

If they can find no errors, they will be sufficiently impressed. If they do find errors, you can be appreciative and they will feel useful for having found and taught you something and you need not be embarrassed, only thankful.

Answer 2

There are really only two ways to do this. One is that you do it all yourself, and the other is that you get some help. You've indicated that you don't think you have the capability to either check it properly or express it in English, so it seems clear that you need help.

The best help would come from someone who you know, such as a professor, given your other issues. And it wouldn't be terrible if they point out an error. That might lead to additional insight that could serve you well..

But once you have it in reasonable shape, there are math journals that will publish student work. If it is truly good, as judged by your professor, you might be able to submit to a regular math journal. If you reach that stage you will get some additional advice from reviewers to further refine it. But it needs to be in fairly good shape first.

Just publishing it, yourself on something like ArXiv seems like a bad choice here if it still is in only preliminary shape. If it has flaws then you might not like the feedback you get.

But your local math professors should support you in this. They can also give you some advice about future directions. Don't underestimate the value of that.

Answer 3

So I don't want to share this with anyone I know unless the proof is reviewed by expert mathematicians and I'm fully sure it's correct or at least seems to be.

This sentence seems to be a bit contradictory in itself. I'm assuming you meant

So I don't want to share this with the mathematical community I know unless the proof is reviewed by expert mathematicians and I'm fully sure it's correct or at least seems to be.

First of all, since you are new to the world of academia, it's reasonable that you are worried about having proper authorship. However, I don't think there is anything to worry about here. Just follow these steps

1. Contact a professor of your university who is expert in the area pertinent to your proof. An email such as follows will suffice

Dear Prof. [name],

While working on [...] I found an interesting approach for proving the Theorem [...]. As far as I am aware, this is still an open problem, so I would be interested in knowing if my attempted solution actually constitutes a proof (or at least if it's a valid step towards one).

Would you be interested in discussing the details via a Skype/Zoom call? I could also send you a draft of the attempt if you like.

Best regards,

Sally Sullivan

You could also mention that you'd like to make it into a publication if the proof is correct or salvageable. But that would be of course implied. Saying it explicitly could sound a bit arrogant to some professors.

2. If the professor agrees s/he will likely find room for improvement. Or will discover an irreparable flaw. We don't know. In any case, based on the amount of work done, s/he might suggest to

   a. Publish a coauthored paper with you and him/her

   b. Publish a solo paper with your name only (in that case acknowledge the professor at the end)

   c. Not publish anything at all

3. If a. or b.: you are in business! If c., you might try to publish anyway, but this is absolutely not recommended, you might regret it later on. Rest assured that, even if the professor contributed a sizable amount, it's still possible that s/he might propose b. There have been several cases where I've seen this happening (albeit for PhD students).

4. If a., when the peer review arrives, the professor will likely take care of that. If b., you'll be the corresponding author, but you can (should) still ask the professor for help.

This was the by far most likely scenario. Now let's review some less likely ones that might make you worried.

1. The professor doesn't want to know anything about it. In this case you can look for a different professor. Or contact a post-doc in your department. You might not know them personally, but the likelyhood of not finding anyone willing to listen is low. If you don't find anyone, I don't really have any smart solution.

2. The professor "steals" your work. That is, s/he publises the proof without giving you credit for it. I find this extremely unlikely, almost unprecedented. There is nothing to gain for a professor to publish one more paper after they have tenure and there is everything to lose if they are found out about it. If it really happens (I highly doubt it will) you have all the e-mail trail and you can prove that you initiated this dialog with the professor. Usually in every university there is a professor who is sort of a reference point for students (when they have complaints etc..). Go to him/her and explain the issue. I'm sure justice will be made.

3. You're afraid you will look like a fool for attempting to present an incorrect proof to a professor. Don't worry, this won't happen as long as you don't make any assumptions prior to presenting the attempted proof. It's perfectly reasonable to make mistakes. Worst case scenario, your attempt would be equivalent to the question "why is this not a correct proof? Where is the mistake?". This is a valid question and you absolutely have the right to ask it as a student.

Also let me comment that your situation is not unique. I have witnessed other cases of master students publishing before their thesis. I do not know the details but they had a professor who helped and they got credit for it.

Let me also give a personal viewpoint. In academia we need to work under the assumption that we are all on the same team. Our goal is to get mathematics done, not to get to be the the one who says "first!". The latter attitude would lead to people keeping secrets and severely impair collaborations. Again, it's pretty reasonable for you to worry about this, but try to learn to free yourself from these concerns as you mature as a researcher.

Answer 4

Such things are quite simple in our day and age. Although you will request help from any professor both for translation and for initial review, you will make sure that you are the first recorded person to post this proof even if it's in your own language. Simply create a transaction in either the Bitcoin blockchain or the Ethereum blockchain with that information (Bitcoin blockchain allows for adding extra metadata in your transaction, the first transaction ever has a phrase the creator left).

If you don't know what a blockchain is, first read up on it, but the gist is that it is a secure and unhackable way to store data in a "cloud" type storage. No professor or university could hack it. If you don't want the proof to be visible, you can always encrypt it and post the encrypted version.

EDIT: I found a service that does just that in a relevant question: proofofexistence.com

Answer 5

Write up a rough draft of the proof, create a public Github repository, and upload the pdf. The Github commit history functions as a publicly-verifiable timestamp. Yet you can always delete the repository if the proof turns out to be wrong. Your work doesn't yet belong on Arxiv, and such uploads are hard to take down.