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This is related to my previous question: “What is the optimal number of times one should meet one's PhD. advisor?”

  • I want to know of specific details of advisor-student meetings, frequencies, patterns in very high-end theoretical subjects like say algebraic geometry or string theory. Like if anyone knows of accounts of how it goes for say students of Vafa or Witten or Nima or Seiberg or Xi Yin or Kiran Kedlaya or Mattihas Zaldarriagga or Bjorn Poonen and such.

  • In such subjects how does one keep oneself motivated since publications aren't so regular probably and progress is possibly very "slow"?

I mean, in such subjects how does one measure progress on a daily/weekly basis to understand if things are going well? (once the instant gratification of homework scores are removed, in full time research mode how is progress measured on weekly scales?)

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    To what extent is work in these areas driven by the reading - contemplation - discussion cycle that seems to be common in the theory driven humanities? – Samuel Russell Apr 16 '13 at 1:33
  • Tough to say. I intersect with CS/Engr/Psyc, but only a little with pure math/probability theory. All of my fields I touch tend to do quite a bit of meetings to hash out big ideas, theory, or implementation details (e.g., weekly or biweekly at least). I didn't see the read-contemplate phase as being distinct: you'd read as you went along and shared as was relevant or felt people should be informed. More like a read-discuss-contemplate cycle. – Namey Jul 27 '13 at 18:54
  • I'm also not sure how "slow" between publications matters. Engineering can be VERY slow between pubs sometimes (imagine having to prove it, then build it, then test it). The issue is the measurement of progress. Proofs are like trying to move a Rubics cube from one state to another, in my opinion. You don't know for sure if there's a way to transform it into the new state until you show it. A set of transformations that might seem to be leading there might run into a dead end (no way to justify a certain leap). Design is often much simpler, as it's modular so you see forward progress. – Namey Jul 27 '13 at 19:00
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Once the instant gratification of homework scores are removed, in full time research mode how is progress measured on weekly scales?

There are three ways to make progress.

  1. The big picture: identifying problems to work on, conjectures and consequences, outlining potential proof techniques.

  2. The little picture: examples, computations, completing the proofs of individual lemmas.

  3. Background reading/study: figuring out what you need to know and learning it.

In any given week it's reasonable to expect some progress on at least one of these. It might not be dramatic or important progress, but at least you can work out some more details for a key example or read another chapter in a book you need to get through. You can also refine your ideas, for example by identifying obstacles or additional ideas for a proof outline. This sort of progress is on a much smaller scale than a research paper, but it lets you measure your progress and ensure your research is on track.

It might occasionally happen early in grad school that you spend a week feeling bewildered and completely unsure of what to do, but at that point your advisor should intervene and help you find something productive.

I want to know of specific details of advisor-student meetings, frequencies, patterns in very high-end theoretical subjects like say algebraic geometry or string theory.

I don't think this would be as illuminating you as hope. There's not a lot to learn from these patterns, and what you do learn could even be misleading: one advisor's approach might be a poor fit for another advisor, and a famous researcher may or may not be a wonderful advisor.

However, if you are looking for examples, Kiran Kedlaya and Ravi Vakil have descriptions on the web of their advising styles. (As one would expect, they differ in some respects, for example on meeting schedules.) Some of the details are probably relevant only if you are considering them as possible advisors, but both pages contain some excellent advice that is more broadly applicable.

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    It might occasionally happen early in grad school that you spend a week feeling bewildered and completely unsure of what to do — The phrase "early in grad school" is redundant here. If you're lucky, you'll have these confused weeks throughout your entire career. – JeffE Apr 16 '13 at 16:55
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    @user6818: I think you are more worried than you need to be. You definitely don't need to write 10 papers in grad school to get a good job in algebraic geometry (the number of people who can do this each year is tiny). One good paper is enough to get a research postdoc, and if you can write several good papers you are doing great. You are right that the three things I mention aren't automatically sufficient to write papers, but they are necessary, so there's no way to avoid this. It's important to keep writing papers in the back of your mind, but not to let it take over your life. – Anonymous Mathematician Apr 21 '13 at 23:35
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    The issue is that to have a strong research career, you need to do things that aren't focused on short-term paper writing. You need to explore ideas that might fail. You need to learn things just because they're interesting (if you haven't already studied something before you need it, you may not even recognize where it could be applied). You need to play with ideas and see where they lead you. You're right that it's important to write papers, but if you do only things that contribute directly to writing papers now, it will limit what you can achieve in your research. – Anonymous Mathematician Apr 21 '13 at 23:40
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    So it's important to be productive, but productivity is broader than just what contributes to a paper this month or even this year. – Anonymous Mathematician Apr 21 '13 at 23:43
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    @user6818: I don't know what sort of publication track record is typical in physics grad school (and it probably differs a lot from mathematics), but ten publications is an extremely large number for an algebraic geometry grad student. As for reading, you certainly don't want to do so much of this that it distracts you from research, but never learning anything not directly related to a current project seems too far in the opposite direction. In any case, I'd recommend doing what your advisor and other successful people in your research area advise. – Anonymous Mathematician Apr 22 '13 at 0:10

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