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Which math is most useful? Differential Equations Statistics / Stochastic Processes Discrete Math / Algorithms / Logic Solver You do not need CT for all this
by hackandthink 4y ago
Which math is most useful?
Differential Equations
Statistics / Stochastic Processes
Discrete Math / Algorithms / Logic Solver
You do not need CT for all this stuff.
Grothendieck needed CT - ist Algebraic Geometry useful?
I've read the paper. They list many useful applications.
CT doesn't seem really necessary for each of them but it looks like CT is (could be) helpful.
- orbifold 4y agoTo properly talk about compositionality in differential equations you absolutely need category theory. Likewise I firmly believe that PDE and numerical mathematics actually lack a good foundation in category theory, not that they don’t need one. It is just very hard to create non-trivial general theories in sich „Applied“ fields, Functional Analysis alone is not very exciting. For an example see for example the work or Hairer (stochastic differential equations) or Costello (QFT).
- hackandthink 4y agoGrothendieck stacks in QFT, did not know about it. This is wild stuff: https://people.math.umass.edu/~mirkovic/0.SEMINARS/1.QFT/C.Costello/Perturbative.QFT.pdf https://people.math.umass.edu/~mirkovic/0.SEMINARS/1.QFT/C.C... funny names: a Leonard Cohen writing about an Costello (but Kevin Costello not Elvis Costello)