A Good Lemma Is Worth a Thousand Theorems

Written: Aug. 14, 2007. Theorems are nice, but they are usually deadends. A lemma may be "trivial", or easy, to prove, once stated, but if it is good, its value far surpasses even the deepest theorems. Wiki has a fairly long list of lemmas, including the powerful Schur's Lemma, Lovasz's Local Lemma, and many others. But my absolute favorite, that lead to at least two Fields medals (so far), is Szemeredi's Regularity Lemma. (see also the beautiful Komlos-Simonovits exposition). Its significance..