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Last active Sep 14, 2018
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Philosophy of supervision

Some thoughts on supervision

As a PhD student you are optimising for a goal with a long time horizon (in the first case to complete a PhD, but then perhaps also to obtain a permanent research position, which could take much longer) and it is hard to determine the correlation between any given intermediate action and eventual success (whatever you define that to be, but two large components could be prove beautiful theorems and get a job). This brute fact lies at the root of much stress and uncertainty. How does one prove beautiful theorems? How does one get a job?

Well, who knows, but certainy not by trying to directly optimise for a goal with a decade long time horizon, and this degree of uncertainty! You have to develop shorter term proxy goals, and it seems to me that part of the job of a supervisor is to assist in that development. If you want to prove beautiful theorems and get a job, then since it is difficult to infer from first principles the algorithm for doing either of those things, a reasonable approximation might be to emulate those who you observe to have proven beautiful theorems and gotten a job. So what would that look like?

Ignoring administrative work, mathematicians spend their time doing one of three things: talking to other mathematicians, teaching, and proving theorems. Those are not distinct categories, obviously. So to a reasonable first approximation your proxy goals should therefore revolve around:

  • Talking: have regular meetings with your supervisor, and try to surround yourself with other (focused, productive) students. A primary purpose of talking is error correction: a good collaborator is a collaborator who ruthlessly, but in a friendly way, puts their finger directly on your confusion. That's uncomfortable, but get over it: nobody proved a beautiful theorem or got a job by prioritising comfort.

  • Teaching: give seminars in front of smart audiences. This develops discipline and helps to avoid fragility (you learn to internalise the ancitipation of the obvious questions relevant to a given piece of material, which you may be too lazy to do if you not know you will have to face an audience later).

  • Proving theorems: reading the proofs of old theorems, and DOING EXERCISES (being good at reading proofs is not very highly correlated with either proving beautiful theorems or getting a job. But doing exercises is very very highly correlated with both of those things).

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