OpenAI and Anthropic Say AI Refuted a Key Computer Science Hypothesis

By Economy Media Newsroom · October 27, 2026

OpenAI and Anthropic, two of the world’s leading artificial intelligence developers, each say their AI systems have disproved the Exponential Time Hypothesis, a decades-old assumption about how hard certain logic problems are to solve and one that hundreds of computer science papers rely on. The claims, released on Oct. 26, have not yet been independently verified, and the researchers who first proposed the hypothesis are now leading an open review of the work.

What the labs are claiming

OpenAI said its internal models produced three research results at once: a disproof of the Exponential Time Hypothesis, known as ETH, in computer science; a proof of a major conjecture in mathematics; and existence proofs for certain theories in particle physics, according to coverage by Unite.AI and the crypto and tech outlet ForkLog. The company said the computer science result was also checked with Lean, a software tool that verifies mathematical proofs line by line.

According to Unite.AI, OpenAI’s documentation says its system wrote the disproof in natural language on Oct. 16 and formalized it in Lean the next day. The result describes a method that, for a fixed class of logic formulas, exactly counts the number of ways to satisfy them in what researchers call “sub-exponential” time, meaning faster than the exponential growth ETH says is unavoidable.

Hours after OpenAI’s announcement, Anthropic posted its own refutation of ETH on GitHub, TechCrunch reported. That release came after Levent Alpöge, a mathematician at Anthropic, publicly suggested that OpenAI’s solutions relied on pre-existing work. TechCrunch said OpenAI’s result does build partly on earlier research, though the dispute has not been settled.

Why the hypothesis matters

ETH was first stated in 1999 by Russell Impagliazzo and Ramamohan Paturi, computer scientists at the University of California, San Diego. It holds that a classic family of logic puzzles, called satisfiability problems, cannot be solved much faster than by trying every possible combination of answers, so the time needed grows exponentially as the puzzle gets bigger.

The hypothesis is closely tied to P versus NP, one of the most famous open questions in mathematics, which asks whether every problem whose answer can be checked quickly can also be solved quickly. Most researchers believe the answer is no. ETH is a stronger version of that belief, and scientists have used it to show that problems in areas such as graph analysis, databases and computational biology are probably hard, ForkLog noted.

If the new results hold up, many of those findings would need to be revisited. Ryan Williams, a professor at the Massachusetts Institute of Technology who studies computational complexity, told TechCrunch that scientists might now give the possibility that P equals NP “a little more weight,” and that intuitions about how hard such problems are may need rethinking.

Several important limits apply, however:

• Refuting ETH would not settle P versus NP, and it does not produce a fast, practical method for solving hard problems, ForkLog reported. A sub-exponential running time can still be extremely long in practice.
• OpenAI itself said that turning the theoretical advance into practical improvements “will require significant further research,” according to Unite.AI.
• Williams told TechCrunch that OpenAI checked whether the result breaks any cryptographic systems, which depend on certain problems staying hard, and was reasonably confident that it does not.

How the work is being checked

The release follows weeks of tension between OpenAI and academic researchers. Earlier in October, mathematicians criticized the company for publishing AI-generated proofs with little advance review, and Williams described one such release to TechCrunch as a “DDOS attack on mathematicians,” a reference to a type of cyberattack that floods a system with traffic.

This time, OpenAI used different approaches for each field. The math results were posted openly on GitHub. For the ETH result, a working group led by Impagliazzo, Paturi and Williams will review the work in the open with the wider community. OpenAI agreed to make all raw data public and to fund a conference on the implications, according to Unite.AI and TechCrunch. The group stressed that its involvement “should not be taken as an endorsement” of OpenAI’s conclusion, ForkLog reported.

In physics, a group led by David Gross, who shared the 2004 Nobel Prize in Physics, will decide how the results are released. OpenAI said the groups work without nondisclosure agreements and that it does not seek academic credit for its models’ discoveries.

What comes next

Williams told TechCrunch that the proof contains “two or three alien-looking parts,” which is one reason he believes the field needs to study it together. He also said he doubts OpenAI’s algorithm is the best one possible and called the work “probably not the final answer.”

Neither lab’s claim has gone through peer review, and no outside group has yet confirmed either proof. Until that happens, the results remain company claims. Williams said he is hopeful about AI-assisted science but worried about how future researchers, especially in pure mathematics, will be trained as machines take on more of the work.