On October 26, OpenAI published three results produced by internal models: one in harmonic analysis, one in complexity theory, one in quantum field theory. The second is the one everyone is talking about. The Exponential Time Hypothesis, or ETH, is false according to OpenAI — proved by its own system, then formalized and verified in Lean.
Why this one conjecture carries so much
The ETH is a conjecture about the computational complexity of Boolean formula satisfiability, which puts it close to P vs. NP. Almost everyone believed it. Hundreds of papers have built conditional hardness results on top of it, across graph theory, computational biology, databases and computational geometry. If the assumption falls, all of those bounds are back on the table, and with them the question of how much faster the affected tasks could get.
OpenAI says the system found its natural-language disproof on October 16, with the formalization coming afterwards. Both the natural-language proof and the Lean version sit in OpenAI’s GitHub repository.
Three results, three release paths
Almost more interesting than the mathematics is how OpenAI is handling it. The company calls the manuscripts “a form of raw research data” and asked outside experts to act as shepherds and form working groups. Those groups recommended three different paths. For the math result, the model output is simply published. For the computer science result, an external group forms to explain it while the output stays public. For the physics result, the group decides what comes out and when — it is holding the artifacts back for now and writing the thing up itself.
Four principles govern the collaborations: no nondisclosure agreements, no academic credit for OpenAI, recognition for the group, independence. Participation is voluntary and unpaid.
The ETH group is led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego and Ryan Williams of MIT. Impagliazzo and Paturi, together with Francis Zane, proposed the hypothesis themselves; Williams has refuted strong versions of it. The group extracted two commitments: all raw data public so the community can verify independently, and a conference funded by OpenAI on what the result means for the field.
The verification is the actual news
A model solving an open problem has become a recurring event. What is different here: the people whose conjecture is said to have fallen are sitting in the group working through the proof, and they insisted on the raw data instead of accepting a press release. That is the shape in which claims like this can be checked at all — and it was not OpenAI’s idea, it was a condition the shepherds set. Until the group is done, the ETH is a result with a Lean seal and no outside reading.