A Good Lemma is Worth a Thousand Theorems: Doron Zeilberger on Mathematical Impact
By
susam
A baker's-dozen of insight crammed into one ring.
Summary
Doron Zeilberger's 82nd opinion piece argues that good lemmas are more valuable than theorems, using Szemerédi's Regularity Lemma as his prime example. He contends that while theorems are often dead ends, a powerful lemma can lead to multiple major discoveries (like Fields medals) and has far greater lasting impact in mathematics.
Key quotes
· 3 pulledTheorems 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.
But my absolute favorite, that lead to at least two Fields medals (so far), is Szemerédi's Regularity Lemma.
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