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I am currently applying for a PhD position in mathematics and during the corresponding interview, I am supposed to give a short 10 minutes talk about my research proposal. In my particular case, my proposal basically aims at generalizing a (very) recently published result from a mathematician of the department I am applying to (who I would like to have as a supervisor). More precisely, my proposal aims at trying to prove the same statement by weakening the requirements, which, however, requires new tools from the beginning.

Since 10 minutes are rather short, I have the following question(s):

As far as I know, a talk given in a PhD interview should usually aim at explaining the things on a rather basic level, so that also non-experts of the field can follow the basic ideas (am I right?). So, since 10 minutes are rather short, I will have to explain some of the basics first. Afterwards, I should probably explain the recent work, since in the end my proposal aims at generalizing this paper. However, all of this is already quite dense, so I won't have to much time to explain my actual proposal, i.e. the steps I have planned to prove the stronger statement.

So, is it fine when most of the presentation is on more basic things, aiming at explaining the basics, the current literature as well as the paper on which my work will be based, or should I shorten this part and work out more the steps I planned in order to achieve my objectives (which is rather hard, as I only have a vague plan, since the precise steps will come when actually working on the project as a PhD student)?

EDIT: This question is not duplicate to PhD interview - short (!) presentation. My question is about a presentation for a proposal, whereas the linked question is about a presentation on an already completed research project. These are two totally different things. In the latter case one can obviously talk about obtained results, which is not possible when presenting a proposal.

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    Does this answer your question? PhD interview - short (!) presentation
    – shoover
    Jul 1, 2022 at 20:36
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    Not really. The question there is about a 10 minutes presentation on a completed project. That is a totally different thing as presenting a proposal for a project you will do in the future (there are no results or so what I can present).
    – B.Hueber
    Jul 1, 2022 at 20:39
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    Will you have an opportunity, before the 10-minute presentation, to talk privately with the professor who you hope will be your supervisor? If so, you might use that opportunity to explain your idea, and then aim the 10-minute talk at the rest of the interviewers.
    – Andreas Blass
    Jul 2, 2022 at 2:04
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    There is something strange about this since in a lot of areas of pure maths it is entirely unrealistic for a PhD applicant to have a viable research proposal at the time of application. Is it possible that the wording in the invitation to interview is a university-wide requirement and your interviewers in maths are not really expecting to hear a fully worked-out proposal during the interview? It would be wise to check this with your potential supervisor first.
    – David Loeffler
    Jul 2, 2022 at 6:23
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    At least in my area (algebraic number theory) I'd be quite suspicious of an applicant who claims to already know exactly what they're going to work on, since it would tend to suggest that they have an unrealistic estimation of their own present knowledge, and are underestimating the hill they'll have to climb to get to the research frontier.
    – David Loeffler
    Jul 2, 2022 at 6:27

3 Answers 3

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There are other ways to handle this, so treat this post as nothing more than something to consider. Note, however, that the person you most want to appeal to already has the background.

Consider starting with the original theorem and say that you see the possibility to generalize it by extending the work on the prerequisites. Then, having set the tone you can work backwards to the underlying theory.

In other words, invert the presentation, starting with the conclusion and working backwards from there. In fact this might actually work in a more general case.

Then, if the clock cuts you off you will have already stated the most important things, rather than the least. And, practice your presentation with a colleague so that you have a good sense of the time limitations and what you can do.

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    Yes, "work backward"... :)
    – paul garrett
    Jul 2, 2022 at 3:18
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    And yes, practice. Don't let the clock cut you off.
    – Bob Brown
    Jul 2, 2022 at 15:05
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I think it's not possible to "explain the basics first", and fit it into 10 minutes. It is just not possible to explain anything non-trivial to "outsiders", in a few minutes.

I'd recommend stating precisely and very succinctly what you propose, without any background at all (after all, some people in the room will understand it...) ... promising to explain that background "as time allows". And, before "giving definitions" at all, succinctly state the "prior art". Then... oop, the time will be up.

Yes, that is frustrating, and may seem perverse, and, well, it kinda is perverse, but I think that what I described is the sanest reaction. Trying to "explain" is doomed, anyway, plus, you'll not get around to telling anything about your actual idea.

And, in any case, do not go overtime. Stop a few seconds early, just to show that you can! :)

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  • Absolutely "Stop a few seconds early!" One of my very favorite students of all time stuck a hand up and asked, "Dr. Brown, what time do you think this class is supposed to end?" Oops.
    – Bob Brown
    Jul 2, 2022 at 15:08
  • I like this but, subjectivity of the question noted, actually recommend being fairly imprecise, high level if possible, and lean heavily on pictures if at all possible. I did one of these types of things for a postdoc with exactly 3 slides and it seemed to go over well.
    – user137975
    Jul 2, 2022 at 15:12
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Not sure if it is good for maths, but in other subjects you could describe first how important the field of work is. Like out of what the original research started, how many first tier papers are published. Then what the grand vision is: why is this interesting? Like if we could do that and that we can prove riemann hypothesis. Then you can zoom back in on the latest result and explain a little in which direction you aim to extend it.

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    I do not think this is a good idea in math. If I heard someone talk bring up how many papers in this field were published in some top-tier math journals, I'd feel like they are wasting my time even if it were far from what I know. Indicate why the topic is interesting, sure, but not by where work is published.
    – KCd
    Jul 2, 2022 at 21:56
  • @KCd are you in one of the lucky departments where funding does not depend on first tier publications?
    – lalala
    Jul 3, 2022 at 13:33
  • It doesn't matter. It would sound strange to me for someone to name-drop journals in a presentation in order to explain why some area of math is worthwhile (sounds like an inferiority complex): "the study of Galois representations led to the solution of Fermat's Last Theorem" sounds normal, but "in the last 10 years there were X papers on Galois representations in Inventiones Mathematicae" does not. What can I say... mathematics has some habits that are different from other subjects, e.g., no special attention to the order of author names on a paper: alphabetical order is standard.
    – KCd
    Jul 3, 2022 at 13:53

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