An opinion piece on Hacker News argues that lemmas, not theorems, drive mathematical progress. While theorems often mark endpoints, a well‑chosen lemma can unlock entire families of results. The author cites classic entries such as Schur's Lemma and Lovász's Local Lemma as evidence of this hidden power.

The writer’s favorite example is Szemerédi's Regularity Lemma, which has already underpinned two Fields medals. Tim Gowers and Jennifer Chayes each devoted a Hedrick lecture to its impact, and the recent Green–Tao breakthrough on arithmetic progressions in the primes relied on a hypergraph extension of that lemma.

Beyond pure theory, the piece collects praise from mathematicians who see lemmas as workhorses. Paul Taylor is quoted saying lemmas do the heavy lifting while theorems collect credit, and Kevin Buchin points to Aigner and Ziegler’s description of lemmas as beautiful, obvious tools that survive paradigm shifts.

The author concludes that lemmas, when broadly applicable and aesthetically pleasing, become the true milestones of mathematics. By framing them as the “real” goals of a mathematician’s career, the essay invites readers to re‑evaluate how research credit is assigned and to hunt for the next universally useful observation.