OpenAI on Tuesday announced three "major" discoveries it says it made in mathematics, computer science and physics, less than a month after releasing hundreds of manuscripts the company claimed contained solutions to long-standing math questions, according to The Verge.
The most striking claim concerns the Exponential Time Hypothesis (ETH), a widely trusted conjecture in computer science. OpenAI says its AI produced a proof that ETH is false, a result that would upend a core assumption researchers have relied on since the hypothesis was proposed in 1999.
What OpenAI says it discovered
The three results were posted to GitHub today. The first, on Local smoothing for the Euclidean wave equation, uses an auxiliary partial differential equation to establish Sogge's local smoothing for waves in every spatial dimension of at least two, according to OpenAI's write-up. It also yields the Kakeya maximal and dimension conjectures and Stein's spherical restriction estimates across the interior of the conjectured range.
The second is the ETH claim. According to OpenAI, the paper gives a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space, with the 3-SAT case refuting the Exponential Time Hypothesis.
The third, in physics, has not been released in full. OpenAI describes it as a "mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics."
- Math: Local smoothing for the Euclidean wave equation, also yielding the Kakeya maximal and dimension conjectures and Stein's spherical restriction estimates



