I'm fourth year undergrad student and I've noticed the skills that I've built up to do computation isn't actually being used.
A good example is algebraic topology, I've never really used calculus in it or PDEs technique. It just seems everything that has been developed is useless to algebraic topology. Only thing I use is group theory and then most of it like common sense reasoning with pictures and heavy use of category theory.
So the soft question is, what computation do you need in algebraic topology/algebraic geometry? As it seems you need none apart from group theory and commutative algebra in AG. Algebraic topology seems to be more understanding as opposed to calculation.
What should really asked is this. What mechanical skills do you need in high end Algebraic topology and geometry. As I've read that Grothendieck didn't know that 57 wasn't a prime and that Bourbaki was saying that you don't need heavy calculations. So was wondering is it worth it to revise all of analysis and skills like solving PDEs, relearning Linear algebra e.t.c., when it seems the skills are useless.
Because I really don't want to relearn computations and certainly don't want to relearn analysis and complex analysis. Plus, I've been reading you don't need it. I suppose the big problem is that undergraduate algebraic geometry looks nothing like graduate text books in algebraic geometry. So what computational skills do you need for graduate level AG.