OpenAI announces three science discoveries in math, computer science and physics
The company says the computer science result shows the Exponential Time Hypothesis is false, and experts will check the work.
1999Year the Exponential Time Hypothesis was proposed
The short version
- OpenAI announced three new discoveries in mathematics, computer science, and physics.
- The math result covers local smoothing for the Euclidean wave equation and also yields the Kakeya maximal and dimension conjectures.
- The computer science result gives a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time.
- The physics result is a mathematically rigorous existence proof of certain interacting quantum field theories, including Quantum Chromodynamics, and the full information has not been released.
Why it matters
The Exponential Time Hypothesis was proposed in 1999 and was widely believed to be true, so the claim would change a major assumption in complexity theory. The Verge reports that an AGMAI panel of math advisers recommended that AI companies do not give certain people early access to output. The open letter from OpenAI asks how credit should be shared for checking, fixing and extending AI-generated results.
“The case of 3-SAT refutes the Exponential Time Hypothesis.”
What people are saying
Commenters on Hacker News questioned the headline, saying it leads with the claim that the Exponential Time Hypothesis is false. One commenter called the announced $5 million donation small compared with the cost of verification. Another asked whether the result moves priors toward P=NP, and a reply said the proof appears to cover #3-SAT, not only 3-SAT.