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Home/Research
Research

OpenAI and Anthropic claim to refute Exponential Time Hypothesis

TechCrunch AI·October 27, 2026·high confidence

Why it matters

  • →Challenges the Exponential Time Hypothesis, a foundational assumption in computational complexity theory.
  • →Demonstrates frontier models can discover sub-exponential algorithms for specific NP-hard problems.
  • →Forces immediate re-evaluation of cryptographic security assumptions and academic research foundations.
OpenAI and Anthropic claim to refute Exponential Time Hypothesis
©TechCrunch AI

OpenAI and Anthropic have jointly claimed to refute the Exponential Time Hypothesis (ETH), a fundamental assumption in computer science stating that certain logic puzzles require exponential time to solve. OpenAI initially released solutions to three major problems, prompting immediate skepticism from the scientific community regarding its 'proof dump' methodology. Anthropic subsequently published its own refutation of ETH, lending credibility to the claim that AI models can find sub-exponential algorithms for these tasks. MIT professor Ryan Williams is organizing a collaborative response to verify the proofs and assess potential impacts on cryptographic security, noting that while current findings don't break existing encryption, they challenge long-held intuitions about computational hardness.

Read original

The story around this

Earlier coverage that leads up to this article, and what followed. Lines connect each piece to the closest one after it, converging here.

OpenAI reveals breakthroughs in math and computer science — OpenAI1OpenAI's Astra Solves 10 Long-Standing Math Problems — The Rundown AI2Anthropic AI Model Advances on Riemann Hypothesis — TechCrunch AI3OpenAI claims AI agents solved Navier-Stokes — Wes Roth4OpenAI's Model Solves $1M Math Problem — The Rundown AI5OpenAI claims Navier-Stokes proof via agents — WIRED AI6OpenAI releases 722 math manuscripts from frontier model — The Verge AI7OpenAI releases 722 AI-generated math manuscripts — Wes Roth8OpenAI and Anthropic claim to refute Exponential Time HypothesisAI Formal Verification Startups Gain Traction — WIRED AI9Aug 1You are hereOct 29

How we got here

  1. 1
    OpenAI reveals breakthroughs in math and computer science

    OpenAI · August 1, 2026 · Background

  2. 2
    OpenAI's Astra Solves 10 Long-Standing Math Problems

    The Rundown AI · August 3, 2026 · Related

  3. 3
    Anthropic AI Model Advances on Riemann Hypothesis

    TechCrunch AI · August 11, 2026 · Related

  4. 4
    OpenAI claims AI agents solved Navier-Stokes

    Wes Roth · September 9, 2026 · Related

  5. 5
    OpenAI's Model Solves $1M Math Problem

    The Rundown AI · September 9, 2026 · Background

  6. 6
    OpenAI claims Navier-Stokes proof via agents

    WIRED AI · September 28, 2026 · Related

  7. 7
    OpenAI releases 722 math manuscripts from frontier model

    The Verge AI · October 6, 2026 · Background

  8. 8
    OpenAI releases 722 AI-generated math manuscripts

    Wes Roth · October 7, 2026 · Related

What happened next

  1. 9
    AI Formal Verification Startups Gain Traction

    WIRED AI · October 29, 2026 · Related

Follow this story

Open the full story →

OpenAI claims major proofs in math, CS, and physics

6 developments

  1. Oct 26 · The Verge AI
    OpenAI claims major proofs in math, CS, and physics
  2. Oct 27 · Wes Roth
    OpenAI AI disproves Exponential Time Hypothesis↳ OpenAI claims its AI disproved the Exponential Time Hypothesis using Lean 4.
  3. Oct 27 · TechCrunch AI
    OpenAI and Anthropic claim to refute Exponential Time Hypothesis (This article)
  4. 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.
  5. 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.
  6. Oct 30 · Matt Wolfe
    OpenAI Disproves Exponential Time Hypothesis

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