I'd be lost without computer algebra systems, but the fact that I can often solve equations they can't just because I know what the equations mean drives home just how far these programs remain from being able to solve every problem that (in some sense) “ought” to be easy.
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@gregeganSF I definitely found that Mathematica seemed unable to analytically compute some contour integrals that I could solve by hand without much difficulty when the integrand had a nontrivial structure of branch cuts. On the other hand, that was probably several Mathematica versions ago.
