Jim Propp quotes:

MacPherson told me that my theorem can be viewed as blah blah blah Grothendieck blah blah blah, which makes it much more respectable.

I think some intuition leaks out in every step of an induction proof.

What promotes math progress even more than new ideas are new technical tools and habits of thought that encapsulate existing ideas, so that insights of one generation become the instincts of the next.