10

I've recently come across a math PhD thesis of a student from a prestigious US university in which he just computationally checked, up to a certain bound, a conjecture, without coming up with any new ideas. To me, this would be insufficient to get a PhD, as there are no new insights. I was talking about this with a collegue, who showed me a phd thesis in which the main thesis was a not well-supported conjecture. Hence the question:

how common is for successful PhD theses in math to have "little to no results" in them? Do you know any further examples (of course, without mentioning names, unis, etc)?

Davidmh
  • 21,215
  • 5
  • 60
  • 105
user31119
  • 103
  • 4
  • 4
    Question: what subject was the thesis in? It could be computational mathematics, and the new, novel idea could be the algorithm used to check the cases. – user141592 Mar 01 '15 at 15:01
  • @Johanna The subject wasn't computational math. – user31119 Mar 01 '15 at 21:44
  • 2
    I've been wondering this too. As a Ph.D. student about to finish, I feel like my "results" are quite insignificant. My advisor seems to think what I already have is enough for a these, but I think it's pathetic and similar to the thesis you've described. – Felix Y. Mar 02 '15 at 03:26
  • 1
    @user31119 or maybe it was number theory? I know of a number theory thesis where the student improved upon an algorithm for finding primes, which sounds like it could be a computer science thesis as well. I'm sure there are quite a few cross-disciplinary theses, where the student starts out in one field and then achieves something in the intersection with another field. It's not necessarily a boring thesis just because it left the original field. – Sumyrda - remember Monica Mar 02 '15 at 06:52

1 Answers1

20

Not all theses are groundbreaking. This is true in math as in any other discipline. Oftentimes, an adviser has a hunch that going in a certain direction might yield something interesting, but that turns out to be wrong -- sometimes because the student didn't work very hard, or simply because there is nothing there. For example, in math, the original conjecture might simply have been wrong; it may have been correct but too hard for even a good student to prove; or, maybe most frequently, it is true in some cases for which it was proven but these cases end up looking rather insignificant.

So, from the perspective of a department, what do you do? The student did work, his work ethic was average, nothing of great significance came of it at the end of 5 years, but it wasn't for lack of trying. Some incremental progress was made, but nothing that looks particularly impressive. Do you kick the student out of the program after 5 years? Do you let them work on this for another 1 or 2 years with uncertain prospect? Or do you simply declare victory, bury the topic, and make sure the student graduates in a reasonable time and everyone moves on with their lives?

You will find that this last option happens surprisingly often. The number of real breakthroughs is, after all, rather small.

Wolfgang Bangerth
  • 94,697
  • 7
  • 201
  • 338