{"version":1,"type":"story","url":"https://digestai.news/story/openai-and-anthropic-refute-exponential-time-hypothesis-with-ai-proofs","json":"https://digestai.news/story/openai-and-anthropic-refute-exponential-time-hypothesis-with-ai-proofs.json","markdown":"https://digestai.news/story/openai-and-anthropic-refute-exponential-time-hypothesis-with-ai-proofs.md","slug":"openai-and-anthropic-refute-exponential-time-hypothesis-with-ai-proofs","headline":"OpenAI and Anthropic refute Exponential Time Hypothesis with AI proofs","summary":"OpenAI’s model identified a proof on October 16, which the company rewrote in the formal language Lean and published on GitHub. The claim demonstrates that counting solutions to SAT problems with fixed-condition sizes can be done in sub-exponential time, undermining ETH’s core assumption that exponential growth is unavoidable. Anthropic followed with its own refutation, also verified via Lean, and both labs invited original proposers Russell Impagliazzo and Ramamohan Paturi to review the work independently. OpenAI also contributed $5 million to the Simons Foundation for further research and peer discussion.\n\nThe breakthroughs extend beyond ETH: OpenAI’s model also proved a 30-year-old conjecture in harmonic analysis and validated the existence of a specific quantum field theory linked to the Clay Mathematics Institute’s $1 million Millennium Prize Problems. However, OpenAI clarified that the P vs NP problem remains unresolved, and practical applications are still distant. Researchers like MIT’s Ryan Williams emphasize the need for community scrutiny, framing this as a collaborative effort rather than a solitary AI achievement. The dual verification process—machine checks via Lean and human review by ETH’s proposers—aims to address skepticism about AI-generated proofs, setting a precedent for future claims.","keyPoints":["Both labs invited original ETH proposers Impagliazzo and Paturi to verify results independently, with no compensation or NDAs","OpenAI donated $5 million to the Simons Foundation for peer review conferences and research on AI-generated proofs"],"whyItMatters":"If validated, they could reshape how researchers approach hard problems—but the real shift is the new hybrid verification model, where AI outputs meet rigorous human and machine scrutiny.","category":{"slug":"research","name":"Research","url":"https://digestai.news/category/research"},"entities":{"companies":["OpenAI","Anthropic","Simons Foundation","Clay Mathematics Institute"],"models":["Lean","Claude"],"people":["Russell Impagliazzo","Ramamohan Paturi","Ryan Williams","Vitalik Buterin"]},"firstPublishedAt":"2026-11-04T03:07:00Z","updatedAt":"2026-11-04T03:07:00Z","sourceCount":1,"hasPrimarySource":false,"sources":[{"outlet":"note.com","title":"AI Punches a Hole in a Wall Thought 'Unsolvable'—OpenAI's Refutation of the Exponential Time Hypothesis (ETH) and the Era of Human-AI Verification","url":"https://note.com/moneycafeai/n/n45a19d6177ea?hl=en","publishedAt":"2026-11-04T03:07:00Z","type":"press","primary":false,"lead":true}],"sourceNotes":null,"discussions":[],"thread":{"title":"AI Models Refute Exponential Time Hypothesis","url":"https://digestai.news/thread/openai-model-allegedly-disproves-exponential-time-hypothesis","storyCount":3},"cite":{"text":"Digest AI, \"OpenAI and Anthropic refute Exponential Time Hypothesis with AI proofs\", 4 November 2026, https://digestai.news/story/openai-and-anthropic-refute-exponential-time-hypothesis-with-ai-proofs","publisher":"Digest AI","title":"OpenAI and Anthropic refute Exponential Time Hypothesis with AI proofs","datePublished":"2026-11-04T03:07:00Z","url":"https://digestai.news/story/openai-and-anthropic-refute-exponential-time-hypothesis-with-ai-proofs"},"generatedBy":"Written by Digest AI's editorial model from the linked sources; the sources are the record.","license":"Headlines, digests and key points are written by Digest AI and may be quoted with a link to the story page. Linked articles belong to their publishers. Terms: https://digestai.news/terms#reuse"}