The Fall of the Theorem Economy
How AI could destroy mathematics and barely touch it
“The product of mathematics is clarity and understanding. Not theorems, by themselves.” —Bill Thurston
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. 1
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 .