In short
OpenAI says its AI has proven that ETH is fake—but the "ETH" referred to here is not the one cryptocurrency traders think of.
The company stated that its AI model found a way to disprove the Exponential Time Hypothesis (ETH), a computer science conjecture from 1999.
Now let’s explain what this actually means and what mathematicians are doing.
OpenAI said ETH is fake, and the reaction on Crypto Twitter was exactly as expected. “Damn, algorithmic traders just wiped out $ETH,” posted a user named Takumi on X; Andrew Jiang joked, “Since this came out, Vitalik has been quiet.”
But hold on a second, everyone—here, ETH refers to the Exponential Time Hypothesis, which has nothing to do with Ethereum, Ethereum’s price, or co-founder Vitalik Buterin. So, crypto brothers, you can relax.
OpenAI released a 67-page paper claiming its AI found a way to bypass this assumption, and the person who proposed the assumption is now reviewing the work.
Computer scientists Russell Impagliazzo, Ramamohan Paturi, and Francis Zane proposed the ETH. This assumption holds that the classic logic problem 3-SAT—finding true/false assignments that satisfy a set of rules, where each rule involves exactly three choices—cannot be solved significantly faster than by exhaustively checking all combinations. OpenAI notes that hundreds of papers assume this holds true and use it to prove that problems in graph theory, computational biology, databases, and geometry cannot be solved quickly.
In other words, ETH is like a map showing tasks that computers are probably never able to complete quickly, and OpenAI says its model has just redrawn that map. OpenAI wrote in its blog: “Refuting ETH has reopened the question: just how much faster can these tasks become?” and added, “This may help guide the search for better algorithms.”
The paper, dated October 17 and revised on October 25, describes a deterministic algorithm—one that does not rely on randomness—that can count all satisfying assignments for this type of puzzle in subexponential time, meaning the computational effort grows slower than any exponential function of the number of variables. Counting solutions is more difficult than determining whether a solution exists; therefore, once the harder task is solved, the easier one is automatically resolved as well.
OpenAI said its AI discovered this counterexample on October 16 and formalized it in Lean on October 17. Lean is a tool that mechanically verifies each logical step. All related materials have been posted on GitHub, following the same approach as the 722 mathematical papers it released earlier this month; only 162 of those papers included main results verified by computer.
Impagliazzo, Paturi, and Ryan Williams of MIT are leading an independent review, and they have been cautious in describing their role. In an open letter, the three wrote: “Our involvement should not be interpreted as an endorsement of this claim.” They added: “Such a significant result requires careful, independent scrutiny and must allow for others to reconstruct, question, and build upon it.”
OpenAI stated that participants did not sign nondisclosure agreements, and the work was unpaid; the company agreed to make all raw data public and provided funding for a conference to discuss these results.
Practical returns are still far off. OpenAI wrote, “Significant follow-up research is needed to find such algorithms and translate theoretical advances into practical improvements.” The paper itself notes that this result does not imply that all NP problems can be solved in sub-exponential time, so the P versus NP problem—whether all problems whose solutions are easy to verify are also easy to solve—remains unresolved.
In simple terms, P refers to the class of problems that computers can solve efficiently, while NP refers to the class of problems whose candidate solutions can be verified efficiently. Thus, the P versus NP question—whether all problems with easily verifiable answers are also easily solvable—remains unresolved.
Anthropic also responded by releasing a paper authored by Claude, titled "A 2^o(n) Time Algorithm for 3-SAT," dated October 26. The code repository similarly addresses the ETH problem, stating that an internal research model of Claude discovered this algorithm, and that "this result is purely asymptotic and does not imply practical solvability of formulas."
Claude formalized Fermat's Last Theorem in Lean in September. Terence Tao also anticipated this convergence, writing in September: “We have now seen that even rumors of someone working on a problem can trigger a flood of AI-driven efforts that flatten it before the original research project has a chance to fully realize its potential.”
OpenAI’s recent $5 million donation to the Simons Foundation will fund workshops, conferences, and special projects to help researchers review and build upon AI-generated results.