OpenAI says it has three new results in mathematics, computing and physics

OpenAI announced three results it presents as advances in mathematics, computer science and physics. The mathematical work, released on GitHub, claims to prove the Kakeya conjecture in all dimensions; the computer science work describes a subexponential algorithm for counting satisfying assignments of fixed-width CNF formulas and, the company says, refutes the Exponential Time Hypothesis (ETH). A group led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will examine the proof and published an open letter seeking feedback from the community. The physics result, which has not been fully released, concerns a rigorous proof about quantum field theories with gauge fields and fermions in four dimensions, including quantum chromodynamics.

TechCrunch reported that Anthropic mathematician Levent Alpöge suggested OpenAI’s work was based on prior research, and that Anthropic later released its own refutation of ETH. The Verge reported that researchers welcomed consultation with outside experts but criticized barriers to public scrutiny.