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Comment by tprice7 | Hacker News Reader

Not necessarily. I left undergrad after four terms and self-studied to the point of having published research, giving invited talks, and even being a visiting researcher for three months with my expenses paid.

Links:

http://content.algebraicgeometry.nl/2017-2/2017-2-007.pdf

https://projecteuclid.org/download/pdfview_1/euclid.ecp/1508...

Look for my name (Thomas / Tom Price) on these pages:

https://web.archive.org/web/20170121000748/https:/wwwmath.un...

https://www2.math.binghamton.edu/p/seminars/arit/arit_spring...

https://www2.math.binghamton.edu/p/seminars/arit/arit_fall20...

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And I think abnry is right that you need some motivating problem / project. In my case it was to prove the Riemann hypothesis. Obviously I have not succeeded but I've learned a lot in the process and it has indirectly led me to some good research questions. I think choosing an outrageously ambitious pie-in-the-sky problem is ok if you are patient and don't try to approach it too directly.

Wow, that's remarkable.

As an aside, your work on numerical cohomology appears to have been useful for a new result pertaining to lattices. Given the authors of the followup work it's likely helpful for the study of lattices in post-quantum cryptography.

Are you referring to the "An Inequality for Gaussians on Lattices" paper? They cite my paper, but it's to give an example of an application of their result (which I use), not because they built on it. But anyway, I think it's very fascinating that the people who discovered a key result that I needed for that paper, which could probably be best classified as arithmetic geometry, are mainly computer scientists!

Ah, thanks for the clarification. The computer scientists who work on quantum computational complexity and post-quantum cryptography tend to be much more mathematical than the norm :)

Just curious, were you working while you studied? How did you manage this?

Sometimes yes, sometimes no. Of course I can go into much more depth in my studies / research while not working. I work the minimum amount necessary to pay my living expenses so I can devote a maximum amount of time to freely pursuing other interests, which includes pure math among other things.

There are plenty of people who devote several years of their life to studying, and must pay not only their living expenses but tuition fees as well. In my opinion, those are the people who you should be asking “how did you manage this”.

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