Is discovering a new (and noteworthy) branch of Mathematics not necessarily worth a PhD? [closed]

Question

I'm currently enrolled for a master's degree in pure mathematics. My supervisor agrees with me that I discovered a new and noteworthy branch of mathematics (and rigorously proved the results).

We both also agree that discovering a new branch of mathematics is not a trivial task. I asked him about the possibility of upgrading my master's thesis to a PhD thesis. He says it is theoretically possible to upgrade a Master's to a PhD at our university, but he reckons my thesis does not have enough sustenance for the upgrade. (At our university there is an option to do a thesis-only masters and a thesis-only PhD, without formal coursework.)

He reckons that I would only be able to publish one paper with my current thesis. He also says that he would normally expect at least three publications to come from a PhD thesis in pure mathematics, but because my discovery required a greater than normal amount of creativity, he reckons an upgrade would still be possible if two publications came from my thesis.

Is this reasonable? Is discovering a new and noteworthy branch of Mathematics not necessarily worth a PhD (regardless of the quantity of papers that get published from it)?

Answer 1

For readers here, the question is too abstract. We haven't seen the work. And our opinion is worth exactly nothing if your advisor and the university don't agree.

The work might be great, or good, or OK. The "new branch" might be significant or not. "Noteworthy" is a judgement that hasn't been tested yet in the wider world. We can't make the evaluation. But your advisor has seen it and is in a position to judge.

I suggest that you follow his advice and do what is necessary to complete the degree. It is probably best to move from the MS track to the PhD track, I think, rather than just take the lesser degree and then have to start over. You will probably benefit from taking a bit more time and a deeper look.

You will really only learn of the potential impact of your work by submitting it for publication and letting the wider world have a look at it. Maybe you get a Fields Medal.

Answer 2

Without more details it's obviously impossible to tell from the outside, but in general, the supervisor is usually right. After all they know what their student did intimately, they know what the institution's requirements are, and so on.

Note your supervisor isn't saying your discovery isn't significant. They aren't even saying your work isn't at PhD level. They could very well be thinking of engaging more Masters/PhD students to follow up on what you've done. What they're saying is that you need to do more work (aka: get more results) to be awarded a PhD. Viewed another way, you're like a PhD student who's completed the first year of a three-year program. Said PhD student can't just decide to graduate because the results they got during the first year are robust; they need two more years of work to have enough material for their thesis.

So it's not unreasonable. If you want the PhD you'll have to put in more time. If money is a concern, you could ask if funding is available for you to convert to PhD studies; otherwise you'll have to be content with a Masters degree.

Answer 3

If he says you need more work, do it. If this is a new and significant branch of mathematics, then lots of research should be possible starting with it. Now (before publication) you have a head start on everyone else who will surely jump in to work on it after you publish.