Differentiable manifolds seem to lie at the core of differentiable programming which is supposed to be hot stuff in ML right now. Not sure about Lie superalgebr

Differentiable manifolds seem to lie at the core of differentiable programming which is supposed to be hot stuff in ML right now. Not sure about Lie superalgebras, but finite fields and elliptic curves are useful in cryptography, homotopy seems to find some application in type theory, category theory (or at least abstract algebra) seems useful for languages with ADTs etc. Not saying that you need to know the theory in order to be able to use all of that (probably most people don't, or at least only the most superficial parts of it), but there are enough applications if you take a close look (and then there's all the obvious stuff: graph theory, numerical analysis, optimisation, etc.) I would say, though, that more that the concepts themselves, it's useful to have some modest mathematical maturity, i.e. you know how to formally prove something (even if you don't use it often), you can read a paper, you can digest abstract definitions, etc.