A Good Lemma Is Worth a Thousand Theorems (2007)

I completely agree. Lemmas are simple, obvious, and yet they completely change how you think.

How many proofs cite the Axiom of Choice? How many cite Zorn's Lemma? Which is more important, the axiom that we're relying on, or the restatement of the axiom that allows us to actually prove things?

It is not just mathematics that values simple and obvious ideas that change how you think. We all should value that. Like Stein's Law, "Things that can't go on forever, don't." And Davies' Corollary, "Things that can't go on forever, can go on longer than you think they can."

I guess homological algebra must be worth at least a million theorems, then?

coyoneda lemma has been helping me out (in prod - at FAANG even!) for over a decade

(2007)