Anthropic says Claude model refuted ETH, hours after OpenAI claim
Anthropic says its internal research Claude model found a subexponential-time algorithm for 3-SAT on October 16, about six hours after OpenAI reported a similar result.
Anthropic published research claiming that its AI model refuted the Exponential Time Hypothesis (ETH), roughly six hours after OpenAI announced similar results on hard problems in mathematics and computer science, according to aitimes.com. Both companies said the discoveries were made on October 16.
Anthropic researcher Levent Alpöge said on X that an internal research Claude model found the key algorithm without human intervention on October 16. The company said the AI-generated output totaled 14 million tokens.
Anthropic published a paper titled "Subexponential-time algorithms for 3-SAT" and Lean verification code on GitHub. The paper's author is listed as "Claude (Anthropic)" rather than a person. The proposed algorithm solves 3-SAT in subexponential time, contradicting ETH's premise.
OpenAI said its model found a proof refuting ETH on October 16 and verified it in Lean the next day. The two companies reached similar conclusions independently on the same day with different detailed approaches.
Neither company's claim has yet been finally verified by the academic community, and the result is theoretical: it does not mean real programs will run faster immediately.
Older groundwork
ETH was proposed in 1999 as a core basis for analyzing algorithmic limits in computer science, and has since been used in graph theory, computational biology and databases. According to OpenAI, hundreds of research results rest on it.
Quick answers
What did Anthropic's Claude model claim to prove?
Anthropic said its internal research Claude model found an algorithm, described in a paper titled "Subexponential-time algorithms for 3-SAT," that solves 3-SAT in subexponential time and contradicts the Exponential Time Hypothesis.
Does this mean programs will run faster now?
No. The result is theoretical and does not mean real programs will run faster immediately.
Has the result been verified by researchers?
Anthropic published Lean verification code on GitHub, but neither company's claim has yet been finally verified by the academic community.