8:49OpenAI’s New AI Is Doing Things We Barely Understand
OpenAI's Mathematical Breakthroughs OpenAI has released hundreds of AI-generated mathematical results, including proofs for complex problems previously considered intractable. One claimed proof concerns "irrational triangular billiards," stating that in a triangular room with at least one angle irrational to pi, almost every light ray visits every spot equally. Another claimed proof involves conformal transformations of planar regions with holes, asserting that these holes can morph into perfect circles or points while preserving angles, even in complex cases. The "Why" and "How" of AI in Math A key debate is whether the goal of mathematics is solely the answer (like a black box output) or the elegant process of understanding and learning new methods. OpenAI's proofs are described as "big ball of barf," requiring other AIs to interpret, contrasting with traditional, elegant mathematical proofs that offer new insights. This approach is compared to training a neural network for fluid simulations: it provides a fast answer but not an understandable algorithm. Progress and Accessibility Concerns AI's mathematical capabilities have rapidly advanced from basic arithmetic to solving high-school competition problems, Olympiad challenges, and potentially millennium problems like Navier-Stokes equations. The average computation time for these new results was 3 hours per paper. A major concern is that this advanced AI model is not publicly accessible, limiting its use to a select few researchers. The speaker advocates for open-weight models to democratize access and allow broader participation in advancing science and mathematics. The withdrawal of some papers due to community feedback highlights the need for collaborative verification, even with AI-assisted discovery.















































