6

Some time ago a professor gave me a small mathematics problem for independent research. While doing reading for this problem I found a substantially different but not unrelated problem mentioned in one of the professor's papers. I did this problem instead.

I would have thought that this means that I picked the problem myself from a paper suggested by the professor, but the professor says that s/he "gave" the problem to me because that's how people see it in Mathematics. This sounds strange to me, and if that's what the professor wants, fine. But I'm wondering if this really is normal in Mathematics.

  • 1
    Is there a problem (authorship etc), or do you really just wonder about the definition of "giving a project" ? – Mark May 18 '18 at 20:47
  • 5
    Just go along with your professor; this is not significant enough to be worth annoying your professor about. – Peter Shor May 19 '18 at 1:00
  • 3
    Why did you not just work on the original problem as given ? – Solar Mike May 19 '18 at 5:55
  • 6
    If what is the norm? To use the phrase about "giving a problem"? To someone? It's a common phrase, it just means that they suggested a specific direction of research. It doesn't really mean anything deep, certainly nothing worth arguing over. – Morgan Rodgers May 19 '18 at 6:01
  • 2
    "While doing reading for this problem I found a substantially different but not unrelated problem mentioned in one of the professor's papers." Your prof may see a closer relationship than you do. This may have been stage 2 of the project in mind, so well done for getting there yourself. – erstwhile editor May 20 '18 at 6:53
7

A short answer: first, in mathematics, this is a typical way of speaking, yes. At best, the advisor has a very good idea that the suggested direction will be fruitful, in one way or another, and is not asking for co-authorship (despite traditions in other disciplines).

That is, hopefully it's much more than "just an idea", namely, it is an idea that fits into or extends something that the advisor has thought about for a long-enough time so that the way it should play out is approximately predictable. This is very important side-information! :)

So, yes, I myself "give" my students projects... based on a large context... which I would bet will turn out well, one way or another... and be fairly interesting to experts, and be publishable, and not tend to allow them to be "scooped", and be complete-able within a good time-frame. All those attributes are highly non-trivial (as we say in math) to arrange. Some expertise required.

13

It's research. You set out to build a plane and end up with a space ship. Or a glider -- most often a glider. If you were my student, I wouldn't say "I gave you the problem". I would probably say that I started you on a research direction.

Two years ago, a friend of mine gave me an idea and I tried to follow it. His idea seemed to lead nowhere. At some point, I read some paper I found by accident and found a way to continue his idea that he most likely couldn't have thought about. I did calculations and wrote a paper about it. Because he gave me the starting idea and constantly provided feedback and suggestions, I put him as last author on that paper.

Usually, advisers get authorship that way. In other words, they start you on a problem, and as you progress, they try to guide you and suggest you resources that could help you. You do start with their idea, which is often wrong, you do the work, and get something that is new. If it comes to authorship, some think that it's enough to get it if they just proposed the problem to you and did nothing else. I think that's not ethical, but it's hard for a student to enforce ethics.

The situation is different if the adviser has some strong indication of what the result of the proposed problem should be. That means he already did some work on the problem and needs you to finish. Then he deserves authorship even if he does nothing but point the problem out to you.

So, "giving the problem" and giving you a direction to work in is quite different. In the first case it's like you're a miner, and your boss tells you to continue digging a given hole because there's gold in it. You find the gold, he deserves a cut. But suppose he tells you to dig a random hole. You find no gold, you move to another hole, and find it there. He doesn't deserve a cut in that case, but he deserves thanks for letting you know that digging in a hole might lead to gold.

If it was business, the professor would get nothing beyond thanks, because they usually say that ideas mean nothing, it's only the implementation that counts.

  • This is a good answer about research in general - worth reading by many planning on a research path... +1 from me. – Solar Mike May 19 '18 at 7:02
  • 9
    Usually, advisers get authorship that way. — In some fields; typically not in mathematics. – JeffE May 19 '18 at 18:14
4

As a mathematician, I personally wouldn't care whether I "gave" a problem to anybody or whether anybody "gave" it to me. This means pretty much nothing. The mathematical problems are not owned or exchanged for profit. They are just shared in the hope that somebody may turn out smart enough to solve them. So if your adviser wants to be able to say that he gave the problem to you and you want to declare that you picked it yourself, you two may have as endless argument about it as you wish, but many people would just shrug at all that nonsense.

As to bringing the matter further to the matters of co-authorship, etc., in mathematics, if the professor is any good, he wouldn't insist on, or even suggest a co-authorship to his student unless he did the lion's share of the work himself. He may agree to it if the student offers it though. The standard politeness requires to be generous with offering co-authorships and reluctant with accepting them.

If all your adviser really wants is that you thank him in the paper for attracting your attention to that problem, I would certainly oblige. This costs you nothing and doesn't diminish your credit by any amount (if you care about such things) while it can help him a bit with his promotion score or grant proposal.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.