Democratic proofs or fake proofs? - Jesús De Loera

Jesús De Loera is a professor of discrete mathematics at UC Davis who remembers when doing math with computers could cost you tenure. His problem for FrontierMath involves Littlewood-Richardson coefficients, numbers whose patterns are very difficult to identify. The obvious approaches fail, and he expects AI to stay stuck for at least five years, perhaps a decade. He doesn't fear AI replacing mathematicians. He fears it corrupting mathematics by convincing people they can outsource judgment to a system that hallucinates with perfect confidence. But Jesús isn't rooting against AI. He compares it to the pocket calculator: dismissed by some, transformative for those who learned to use it well. And he offers a surprising take on mathematical proof itself: compared to a human proof understood by only a handful of experts, a computer-verifiable proof that ten undergraduates can reproduce is both more democratic and more valuable. -- Episode links -- Transcript: https://open.substack.com/pub/epochai/p/democratic-proofs-or-fake-proofs -- Timestamps -- 00:00:00 – Introduction 00:01:10 – Using Littlewood–Richardson coefficients to stump AI 00:02:52 – Why the problem should remain hard for AI for years 00:03:36 – AI as an amplifier of human mathematicians 00:05:14 – Can AI ask good mathematical questions? 00:05:57 – What makes a proof “valuable”? 00:09:34 – The risks of overtrusting AI in research 00:12:01 – Will mathematics become more experimental? 00:13:17 – Optimistic and pessimistic futures of math with AI 00:14:33 – Timelines, fears, and hopes for AI progress Special thanks to interviewer Daria Ivanova: https://youtube.com/@inQEDible Recorded in May, 2025.