TITLE: Every mathematician has only a few tricks
QUESTION [156 upvotes]: In Gian-Carlo Rota's "Ten lessons I wish I had been taught" he has a section, "Every mathematician has only a few tricks", where he asserts that even mathematicians like Hilbert have only a few tricks which they use over and over again.
Assuming Rota is correct, what are the few tricks that mathematicians use repeatedly?

REPLY [2 votes]: Taylor expansion. Much of the classical theory of statistics (and some of its modern extensions) revolves around performing a second-order Taylor expansion of the likelihood.