The most exciting claims from OpenAI’s heap of new proofs

OpenAI released over 700 AI-generated manuscripts claiming to solve 372 open problems in mathematics, theoretical computer science, and physics. The proofs are largely unverified, with some retracted due to errors found by outside scientists, and not all certified by the Lean proof assistant. Nevertheless, experts describe the results as jaw-dropping, with some discoveries that could have earned top research awards a year ago. Key claims include major progress on the Riemann hypothesis and the proof of the quasi-Riemann hypothesis, settling questions about Siegel zeros, solving a generalization of Hilbert's 10th problem for rational numbers, proving the four-dimensional Kakeya conjecture, and resolving the nonlinear sigma model analogous to the Yang-Mills mass gap problem. In computer science, OpenAI claims faster matrix multiplication (exponent 2.25), derandomization results (L = RL = BPL), a proof of the unique games conjecture, unitary synthesis for quantum computing, and a minor improvement to the Fast Fourier Transform. While many results are groundbreaking, some papers are considered incomprehensible or sloppy, and full verification will take time.

(Source：Scientific American)