Why is the study of differential equations important for pure mathematics? I understand why DEs are important from a practical view in that they can be used to model many phenomena dealing with change, however why are they important in connection to other areas of mathematics?

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Anonymous Mon Oct 24 03:54:31 2016 No.8433998 [Reply] [Original]

Why is the study of differential equations important for pure mathematics?

I understand why DEs are important from a practical view in that they can be used to model many phenomena dealing with change, however why are they important in connection to other areas of mathematics?

Anonymous Mon Oct 24 04:24:34 2016 No.8434014

That's kind of a stupid question, isn't it?
There are unsolved problems, and why would abything be important for pure mathematics, other than mathematicans being interested in the subjects.
Anyway, it relates to functional analysis, differential geometry, and people like Tao even do Navier Stokes in connection with theoretical computer science.

>>	Anonymous Mon Oct 24 04:40:12 2016 No.8434022 The Thurston geometrization conjecture(ie: Poincaré conjecture) was proven using ricci flow with surgery ie with PDEs

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