[nyssos]

> Much of mathematics is a formal affair of making arguments to satisfy necessary and sufficient conditions.

Some areas have a formalist culture like this (descriptive set theory seems to, for instance, though that might just be what it looks like from the outside), but it's far from universal. At the other end of the spectrum I find it hard to imagine anyone getting far with algebraic geometry without building intuition. And then of course in mathematical physics the intuition-frontier is always decades ahead of the formal one.