The Mathocalypse

Mathematical proofs can now be generated by AI, making them difficult for humans to verify and understand without AI assistance.

OpenAI has released 372 significant mathematical proofs, including a purported proof of Subhash Khot's Unique Games Conjecture (UGC), a problem complexity theorists have worked on for decades. The proofs, generated by an internal OpenAI model, were released with Lean certificates, but human mathematicians are struggling to understand them. The UGC's truth has implications for the hardness of numerous optimization problems. OpenAI's release strategy involved publishing the proofs for the mathematical community to decipher. Alongside the UGC proof, other major results include a proof of L=BPL, faster Fourier Transforms, and progress on the Unitary Synthesis Problem and quantum complexity theory questions. Separately, Anthropic provided an AI model that assisted in solving the 3SUM and All-Pairs Shortest Paths problems, with Anthropic compensating the researchers to produce a digestible version, highlighting different AI-human collaboration models.

The sheer volume and complexity of AI-generated proofs challenge the traditional human-centric model of mathematical discovery and verification. This suggests a future where AI acts not just as a tool for computation, but as a creative partner or even a primary generator of novel mathematical insights, forcing a reevaluation of what constitutes understanding and proof in mathematics.

The contrasting approaches by OpenAI and Anthropic reveal a nascent debate about how AI's mathematical breakthroughs should be integrated into the scientific community. OpenAI's method ignites a competitive race for human interpretation, potentially accelerating understanding but also risking misinterpretation or a loss of human intuition. Anthropic's model, while offering more curated and potentially accurate explanations, introduces a gatekeeping element, raising questions about access and intellectual credit.