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I am a Ph.D. student in pure mathematics with a few published works in my field. I would like to know how Ph.D. students are evaluated by the examiners before the defense. What are essential points to be careful about when writing a thesis? I would also like to know how much time is usually taken from submission to defense.

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    Have you asked your adviser these questions?
    – user137975
    Commented Apr 24, 2023 at 21:42
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    What country are you studying in?
    – Buffy
    Commented Apr 24, 2023 at 21:42
  • @AnonymousM Yes I have asked him but still, I would like to know from other people's perspectives.
    – Hap
    Commented Apr 24, 2023 at 21:46
  • @Buffy I am studying in India
    – Hap
    Commented Apr 24, 2023 at 21:46
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    It will range from "read all proofs closely" to "do not even open." Commented Apr 24, 2023 at 22:10

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I don't know if this is applicable to India, but, since you want a general answer, I can say a few things.

Generally, at least in the US, the expectation is that the thesis is publishable work. In other words it makes a significant and novel contribution to mathematical knowledge. You don't have to solve a famous unsolved problem, but you need to make a definite contribution.

Your thesis needs to show that you have some deep insight into a narrow part of mathematics and that you have the capability to do more, perhaps in collaboration with others.

It should also demonstrate that you can write and express things clearly and correctly.

However, your thesis can be your first significant work, not the most important work of your career, assuming you stay in academia. So, the Riemann Hypothesis is out.


I have no idea about timing. Your committee will need time to do a review, hopefully more complete than a cursory reading. Most of my committee (long long ago) couldn't understand everything in my dissertation, as they were from different specialties, but they could sort of grasp its importance. The latter was partly due to the assurance given by my advisor to them, as he was well respected.

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    "However, your thesis should be your first work" is simply wrong (but true for most students). Commented Apr 24, 2023 at 22:00
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    How about "can be your first significant work", then, @MoisheKohan. That was my intent.
    – Buffy
    Commented Apr 24, 2023 at 22:02
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    Much better..... Commented Apr 24, 2023 at 22:03
  • @MoisheKohan, my "first work" was more than 60 years ago in secondary school. It was published (part of a book) only recently. It won an award back then, but wouldn't have been publishable as a stand-alone (then or now). But it was "insight revealing" and so has pedagogical value for those learning math.
    – Buffy
    Commented Apr 24, 2023 at 22:17
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    Examples I had in mind were Milnor's paper "On the total curvature of knots" (not a part of his thesis, 121 citations on MathSciNet), or John Pardon's undergraduate work, or Drinfeld's HS work... Commented Apr 24, 2023 at 22:30

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