OpenAI Claims Its AI Has Disproved the Exponential Time Hypothesis and Solved Two Other Major Scientific Problems

OpenAI announced on October 27 that its AI models have independently disproved the Exponential Time Hypothesis (ETH), a foundational conjecture in theoretical computer science — and produced two additional mathematically rigorous results covering pure mathematics and quantum physics. If independent verification confirms these findings, it marks the first time an AI system has overturned a major standing conjecture in computer science on its own.

What the ETH Is — and Why Disproving It Matters

The Exponential Time Hypothesis, first proposed in the late 1990s, holds that satisfiability problems — a category central to cryptography, scheduling, optimization, and large portions of modern software — cannot be solved faster than exponential time. Hundreds of proofs in complexity theory rest on the ETH as an assumed foundation. Disproving it would force a significant rewrite of what we understand about computational limits.

According to OpenAI, the AI found the disproof on October 16. The proof was then formalized in Lean — a proof assistant software used by mathematicians to verify that formal arguments are logically correct step by step — the following day. Two of the ETH's original authors have been enlisted to lead independent verification.

The Other Two Results

Beyond the ETH, OpenAI reported two additional findings:

• Local smoothing conjecture: The AI produced a proof of the local smoothing conjecture in every spatial dimension. OpenAI says this proof simultaneously establishes the Kakeya conjecture and the Stein restriction conjecture — two long-standing open problems in harmonic analysis, the field concerned with how complex signals and functions decompose into simpler wave components.

What This Would Mean

Taken individually, any one of these would be a significant result. Together, they represent an extraordinary concentration of claimed mathematical and scientific advances from a single AI system.

The ETH disproof is the most immediately consequential for the computing industry. Theoretical computer scientists and cryptographers have built large bodies of work on the assumption that the ETH holds. A disproof creates an obligation to check which of those dependent proofs still stand — and reopens questions about what computational problems are truly intractable.

The QCD existence proof, if validated by the broader physics and mathematics community, would resolve a problem that has resisted rigorous formulation for decades and would qualify for the Clay Institute's $1 million prize.

What to Watch

Independent verification of the ETH disproof is underway, with the hypothesis's original authors leading the review. The mathematical community will examine not just the proofs themselves but the AI's discovery process — specifically, what scaffolding or prompting was involved and how much of the work was the AI's versus the researchers directing it.

OpenAI has not specified which models produced these results. That detail will matter for assessing whether this is a reproducible capability or a one-off finding.