What would be right course of actions to get both — publication and admission?

Question

I'm in a situation that I've never faced before: I believe that I've found the solution to a classical mathematical problem and would like to get the solution published in a reputed journal. The solution might be wrong as and I'm willing to accept that because I've not shared the solution with anyone yet, but if it is correct (which I hope), it is good enough to be presented in a good journal.

The problem: I want to pursue my masters next year. I'm not a prodigy; hence I've applied to a few good universities but not to the top ones. The journal that I seek to publish my paper in takes 14–18 months on average to accept and a similar time to publish it. Hence, if I want my research outcome to help me apply in some top universities, I'll have to wait that long, hoping my paper gets accepted and published.

I'm a bit protective about my work and wanted to share it with the reviewers of the journal only, but then I got to know about arXiv, where I can publish my paper and it will be visible to everyone. The journal I seek to publish in accepts arXiv-published papers, so that should not be a problem.

Can you please suggest if it is advisable to publish a paper with a potential solution to a classical problem openly on arXiv and then use the arXiv link to share my paper and convince the selection committees about by candidacy?

Is there any other solution to this problem that you'd recommend? This is first time I'm going to publish a paper.

Answer 1

I don't know how admissions works in India so this might be good advice or not.

You don't seem especially certain of your proof. That worries me and normally one would then want to work with a colleague on the issue, and probably share authorship.

However, you can submit the article. If it turns out to have obvious errors you will probably hear back quickly. If they put it out for review you have some chance of success, though it takes time as you note.

While it is out for review, you can have a section of your CV named "Work in Progress" and list this work there. Such a section is valuable to have on a CV most places and helps with admissions but I don't know about India.

Now when you apply for study and send the CV, you might be asked to share the paper with someone in the admissions process. You can do it then, privately, without publishing it on arXiv.

If the journal you send it to doesn't accept it for reasons other than fundamental errors then you haven't compromised it by informal publishing, which other journals might not accept.

Note that publishing on arXiv might get you some feedback on it and attaches your name to any ideas in it, but it will be out there for people to see as it is really a form of publishing.

Answer 2

Hence, if I want my research outcome to help me apply in some top universities, I'll have to wait that long, hoping my paper gets accepted and published.

There are so many ifs (if you submit for pubblication, if it is accepted, if it will be published in 18 months, if it will be considered by the comitee), what you are thinking is too much of a stretch. If you have a publication, it will help your access to university.

• Do you have publications as of today?

No.

• Will you have publications 2 years down the line?

Maybe, so be on the safe side, stop dreaming, consider it a no.

I want to pursue my masters next year. I'm not a prodigy

I am just a random guy in the internet, but you are focusing on having a paper published to access a master, when the real question is "what will you do with your master degree since you are a not-a-prodigy-maybe-a-median student"? Again, thinking about having a paper published in 2 years and getting admitted to the university is the combination of two unlikely events. But it is even more unlikely than "after my average master in an average university I will pursue a PhD in maths, possibly abroad".

Apply for the university you would like to. Plan A is that you get accepted. Unlikely. Therefore, prepare a plan B for the possible rejection. What can you do in the next 18 months to improve your chances of admission? Or what can you do in the next 18 months to sustain economically yourself? maybe you do not need to work full time and you can work on your paper. With that we go to:

I'm a bit protective about my work

Then put it on arXiv. Having it on arXiv, it will be quite difficult to protect your intellectual property, but without having such a timestamp from arXiv, it will be almost impossible, given your conditions (no affiliation, no previous work, no contributions to conferences&co.)

Sorry being abrupt, you are right in pursuing your dreams, but only if you can afford them.