A Good Lemma Is Worth a Thousand Theorems

Mathematician Doron Zeilberger argues that mathematical lemmas are often more valuable and impactful than theorems, despite theorems receiving greater recognition. He highlights Szemerédi's Regularity Lemma as a prime example, noting it has led to at least two Fields Medals and enabled breakthrough results like the Green-Tao theorem on primes in arithmetic progressions. A truly great lemma, according to this perspective, should be widely applicable, obvious once understood, and mathematically beautiful.