# Need for computation in pure Mathematics at the highest level?

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.

Edited:

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.

• What do you mean by "computation"? Sep 15, 2011 at 16:49
• Is calculation of homotopy/homology groups of spheres/computing fibers of a morphism in algebraic geometry etc computations to you?
– user325
Sep 15, 2011 at 16:50
• @Complex: Computations are very important as they help by adding to your understanding of what is going on. However, it seems that your complaint is based on the terrible way mathematics is taught at the lower levels; only computations and no understanding. I don't think you should associate calculus with just pages of computations, but rather how you in particular were taught calculus at that time. Sep 15, 2011 at 17:23
• I think the question is ill-posed and phrased in a contentious way. Sep 15, 2011 at 18:07
• @complex123: I do not understand what point there is in your telling what areas of math you believe are «horrible» and «stupid». You do not seem to be that well versed in them, so we (and you yourself...) should take your judgements of them with a bit of care. Indeed, your argument is more or less based on your not knowing what (what you call) computation is for; do you know what kind of computations are carried out by algebraic number theorists?. If my vote were not final, I would vote to close. Sep 15, 2011 at 20:43