Research
OpenAI AI disproves Exponential Time Hypothesis
Wes Rothmedium confidence
Why it matters
- →AI systems are now capable of verifying complex mathematical proofs that challenge foundational computer science theories.
- →A disproven ETH could imply polynomial-time solutions for problems previously thought to be exponentially hard.
- →This demonstrates a new capability for AI in formal verification using Lean 4, moving beyond code generation.
OpenAI announced that its AI system has successfully generated and verified a formal proof disproving the Exponential Time Hypothesis (ETH), a long-standing conjecture in computer science. The work, documented on GitHub using Lean 4, addresses complex mathematical areas including local smoothing and Kakeya sets, challenging the assumption that certain problems require exponential time to solve. This development marks a significant shift in AI's role from heuristic tool to formal theorem prover, with implications for the P versus NP problem and cryptographic security. The claim has drawn attention from prominent theorists like Scott Aaronson, though independent verification is ongoing.
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Earlier coverage that leads up to this article, and what followed. Lines connect each piece to the closest one after it, converging here.
How we got here
- 1OpenAI's Astra Solves 10 Long-Standing Math Problems
The Rundown AI · August 3, 2026 · Related
- 2OpenAI's Astra Solves 10 Major Math Problems
The Rundown AI · August 3, 2026 · Related
- 3AI Solves Long-Standing Math Problems
The Verge AI · August 11, 2026 · Related
- 4OpenAI Claims AI Solved Major Math Problem
WIRED AI · September 8, 2026 · Related
- 5OpenAI claims AI agents solved Navier-Stokes
Wes Roth · September 9, 2026 · Related
- 6OpenAI's Controversial Win in Mathematics
The Verge AI · September 12, 2026 · Related
- 7OpenAI claims Navier-Stokes proof via agents
WIRED AI · September 28, 2026 · Related
- 8OpenAI releases 722 AI-generated math manuscripts
Wes Roth · October 7, 2026 · Related
Follow this story
Open the full story →OpenAI claims major proofs in math, CS, and physics
6 developments
- Oct 26 · The Verge AI
OpenAI claims major proofs in math, CS, and physics - Oct 27 · Wes Roth
OpenAI AI disproves Exponential Time Hypothesis (This article)↳ OpenAI claims its AI disproved the Exponential Time Hypothesis using Lean 4. - Oct 27 · TechCrunch AI
OpenAI and Anthropic claim to refute Exponential Time Hypothesis - Oct 27 · The Verge AI
OpenAI's math breakthroughs spark researcher backlash↳ OpenAI faces backlash for restricting proof verification to select 'shepherds' despite advisory warnings against gatekeeping. - Oct 30 · The Verge AI
OpenAI doubles down on math AI despite researcher backlash↳ Altman confirms OpenAI holds massive undiscovered math stockpile and prioritizes human access over researcher attribution despite backlash. - Oct 30 · Matt Wolfe
OpenAI Disproves Exponential Time Hypothesis
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OpenAI Disproves Exponential Time Hypothesis
OpenAI researchers published findings disproving the Exponential Time Hypothesis, a major result in computational complexity theory.
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