Ever since the dawn of the “LLMs do math” era, many have independently come up with what I’ll call the “Convex Hull Hypothesis” (CHH). Roughly speaking, CHH states that every AI-generated proof, no matter how complicated it may seem at first glance, is a simple combination of known mathematical ideas. The CHH is often used to argue that AI models are incapable of being “creative” or “original,” or to argue that they must be violating ethical or legal standards surrounding intellectual property.
When Paul Cohen came up with forcing to prove the independence of CH (only one “H” here!), many people quickly found precursors in the literature to practically every ingredient in the proof. I have heard a rumor (maybe a reader who knew Cohen personally can confirm or disconfirm) that Cohen got a bit annoyed, perceiving that others were trying to downplay the originality of his work. Had Cohen been an LLM, undoubtedly many would have loudly insisted that forcing was well within the convex hull of known math.
Here, rather than entangle myself in heated philosophical debates about the truth or falsity of CHH or its alleged corollaries, I suggest that CHH can be a valuable heuristic when trying to gain an initial understanding of a seemingly impenetrable AI proof. That is, don’t start by trying to swallow the proof raw. Start by assuming that the proof is a relatively straightforward combination of ideas that already exist in the mathematical literature. This assumption may or may not be correct, but I believe that it will frequently lead to success, or partial success, and when that happens, it will greatly aid the process of human understanding.
Again, I do not claim that any such “reconstruction” of the AI-generated proof should be accompanied by triumphant cries that ontogeny recapitulates phylogeny. But I do claim that it will help ease the pain of studying opaque AI-generated proofs.
Received 8 October 2026.
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