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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.

22 votes

Why is the Fourier transform so ubiquitous?

To add a representation theory perspective: if $G$ is a Lie group, and $f$ is a function (or more precisely a distribution) on $G$ then (under certain mild conditions on $f$ and $G$), the function $f$ …
Dmitry Vaintrob's user avatar
20 votes

Algebraic machinery for algebraic geometry

I want to offer a possibly heretical opinion based on conversations I've had with people who do algebraic geometry, especially Joe Harris. I think that it is not necessary to know very much commutativ …