GoKawiil“The product of mathematics is clarity and understanding. Not theorems, by themselves.”
—Bill Thurston
Handwritten diagram by Alexander Grothendieck
My best theorem is one I never wrote down.
It crystallized one bright morning in Lausanne, Switzerland, as I was preparing for my last invited conference talk. The proof felt so obvious—and the result so compelling—that I made the reckless move of editing my slides at the last minute. Time was running out and I could only include the announcement as an informal remark at the bottom of the last slide, instead of stating it as a proper theorem.
I had already quit academia and founded a machine-learning startup. I knew I would be too busy to write a clean proof and publish it. That was my excuse for being sloppy. I just wrote the remark and abandoned the slide deck as a message in a bottle.
My hope was that some bright young mathematician would pick it up someday and formalize the result as part of a broader theory. If I lucked out with the intrinsic randomness of attribution, I thought, it might even be remembered as the Bessis cellular decomposition theorem.
But that was stupid. By claiming the result, I had killed the incentive for anyone to write it up.
If I had to pick my second best result, it would be Theorem 0.5 in my old preprint on Garside categories. I had high ambitions for this paper, yet I ended up not submitting it anywhere. The creative process had drained me, and I left active research before regaining the courage to clean up the preliminary sections.
For a second best, this theorem is shockingly easy to prove. Once you get the preliminaries right, it only takes a few pages of pretty terrestrial group theory.
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