OpenAI's AI Models Disprove Exponential Time Hypothesis

OpenAI announced on October 26 that its AI models produced three major research results, including a disproof of the Exponential Time Hypothesis-a foundational conjecture in theoretical computer science used in hundreds of papers. The company also announced proofs of the local smoothing conjecture in harmonic analysis and an existence proof for quantum chromodynamics, all currently under expert review.

OpenAI unveiled three significant scientific breakthroughs generated by its internal frontier models, marking a potentially transformative moment for theoretical computer science and mathematics. The most headline-grabbing result is the disproof of the Exponential Time Hypothesis (ETH), a longstanding conjecture about how fast certain Boolean satisfiability problems can be solved-a problem deeply connected to the famous P versus NP question.

The ETH has been foundational to computational complexity theory for decades, appearing in hundreds of peer-reviewed papers where researchers used it to derive conditional hardness results across graph theory, computational biology, databases, and computational geometry. OpenAI's system produced a natural-language disproof on October 16, 2026, which was then formally verified in the Lean proof assistant on October 17. The company claims to have found a subexponential-time algorithm for problems previously thought to require exponential time-a result that, if validated, would fundamentally reshape assumptions about computational limits.

Alongside the ETH result, OpenAI announced two complementary findings: a proof of the local smoothing conjecture for the wave equation in every dimension (which simultaneously resolves the Kakeya and Stein restriction conjectures), and a mathematically rigorous existence proof for quantum chromodynamics incorporating Yang–Mills theory. The company published the AI-written proofs and Lean formalizations in a public GitHub repository, describing the manuscripts as raw research data.

Crucially, none of these results has undergone independent expert verification yet. OpenAI emphasized its commitment to transparency by organizing groups of outside experts to examine and explain each result to the broader research community. The company noted that while the ETH refutation "reopens questions about how much faster these tasks could become," turning such theoretical advances into practical algorithmic improvements "will require significant further research." The announcement combines genuine scientific ambition with notable caution-OpenAI is explicitly inviting scrutiny rather than claiming definitive proof.