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I am doing my Ph.D. thesis in mathematics. I am wondering if it is a good idea to name some mathematical objects after my thesis advisor. The two objects I have in my mind are:

  1. A representation, whose existence and faithfulness is a main result of my thesis. This representation has not be studied before and thus unnamed.
  2. A collection of subgroups of a certain group, which have been studied by others but with no specific name assigned to those subgroups.

I did not ask this question directly to my thesis advisor since I believe that out of humility he would decline this request. Have asked this question to a mathematics professor from another university, who personally knows my advisor well and he says that it was a very good idea. But he was somewhat drunk when answering my question and I am wondering if I should take his answer seriously.

Edit: The representation I have mentioned is similar but different from a classical representation, which is named after the mathematician Emil Artin. In this case, should I still call it "Artin's representation", or "(my advisor's surname)'s representation", or leave it unnamed?

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    If you need a name for a representation which is similar but not quite like an Artin representation, you can reflect that in a proper name, which contains "Artin" and an adjective describing the change. Jan 30 '15 at 9:17
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    Is it possible for you to talk to that other professor again, when he's sober? Jan 30 '15 at 9:42
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    Well, there's this new-fangled thing called the telephone that might be useful in a case such as this. Jan 30 '15 at 9:44
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    Honestly, I think two factors - the fact that the other professor knows your advisor personally, and that the other professor works in the same field - make that professor much better qualified to answer the question than a bunch of semi-anonymous internet people whose qualifications you can never be sure of. At the very least, he might give you some things to think about - reasons why naming something after your advisor is a good idea, or reasons why it isn't. I don't see the harm in at least talking to him. Jan 30 '15 at 9:54
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    FYI, Buchberger named Groebner bases after his thesis advisor, in his thesis. But the concept was not very closely related to something already named after another person.
    – KCd
    Jan 31 '15 at 0:54
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It sound as though your advisor was not the first to study/define/use these objects, but rather you just want to name them something, and think it might be nice to name them in honor of your advisor. Please don't do this. You'll only contribute to Stigler's law of eponymy, confuse people, embarrass your advisor and/or offend whoever was the first to study these objects.

Bear in mind two things: (i) Not every random object deserves a special name. (ii) When you name objects, name them in a descriptive and evocative way, that will make using the terms intuitive and non-confusing (as a corollary, it also shouldn't conflict with other notation). Many people don't even like the idea of name any mathematical objects after people, though it's common practice.

Now that naming them after your advisor is out of the way, you should feel free to consult your advisor on naming these things.

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    +1. Mathematical objects are not like beetles or asteroids; we don't name them after people just to generically honor them. If a mathematical object takes on the name of a person, it's because there is a consensus in the community that this person deserves the credit for introducing the object. It's not a decision that the discoverer, or even early practitioners, get to make. Jan 30 '15 at 8:17
  • Thanks for the advice! For the representation that I mentioned, theoretically I am the first one to study it in my Ph.D. thesis and my advisor has helped me a lot in the study. In fact, some key ideas in the proof of its very existence are from my advisor. In this case, since it is unnamed anyway, should I name it after my advisor?
    – Zuriel
    Jan 30 '15 at 8:20
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    Zuriel, no, the proper thing to do is credit him with suitable acknowledgements in your thesis/paper. And it's typical that advisors help students with key ideas.
    – Kimball
    Jan 30 '15 at 9:20
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    However, it's possible that his name could get associated with it later by someone else. I recently wrote a paper about a conjecture in someone's thesis paper. He did not name the conjecture after his advisor, but it was clear the advisor had this conjecture in mind first, so I named the conjecture after both of them, even though the advisor's name was not the paper where it was first stated. (I checked with the advisor first (his student is no longer in academia), whom I know, to make sure this was okay.)
    – Kimball
    Jan 30 '15 at 9:25
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    @Zuriel: As I said, I agree that you should not. Make it clear in the paper what his role was in inventing the objects, and choose a descriptive name, but leave it to posterity to decide if they are interesting enough to name after someone, and if so who. Like I said, this is not up to you. (The "interesting enough" criterion is significant too: having something trivial or uninteresting named after you is an extremely dubious honor, and you are not in the best position to judge this.) Jan 30 '15 at 15:01

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