--- title: OpenAI says its AI model has disproved the Exponential... description: An internal OpenAI model claims to have disproved the Exponential Time Hypothesis (ETH), a conjecture underlying hundreds of computer science papers on problem... canonical: https://daily.dev/posts/openai-says-its-ai-model-has-disproved-the-exponential-time-hypothesis-87bfarulu twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: OpenAI says its AI model has disproved the Exponential Time Hypothesis | daily.dev og:description: An internal OpenAI model claims to have disproved the Exponential Time Hypothesis (ETH), a conjecture underlying hundreds of computer science papers on problem... og:url: https://daily.dev/posts/openai-says-its-ai-model-has-disproved-the-exponential-time-hypothesis-87bfarulu og:image: https://api.daily.dev/og/posts/87bfarUlU.png og:image:alt: OpenAI says its AI model has disproved the Exponential Time Hypothesis og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # OpenAI says its AI model has disproved the Exponential Time Hypothesis **[The Next Web](https://daily.dev/sources/tnw)** · 3 min read · 0 upvotes · 0 comments ## Summary An internal OpenAI model claims to have disproved the Exponential Time Hypothesis (ETH), a conjecture underlying hundreds of computer science papers on problem hardness. OpenAI says the model found the disproof on 16 October and checked it in Lean the next day. A group led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego and Ryan Williams of MIT will check and explain the result, but stress their involvement is not an endorsement. The same day, OpenAI also announced AI-produced results in mathematics, including the local smoothing conjecture, and in physics, including a proof that pure Yang-Mills theory exists. OpenAI gave $5 million to the Simons Foundation for related workshops. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Questions this post answers ### What is the Exponential Time Hypothesis and why does it matter for computer science? The Exponential Time Hypothesis (ETH) is a widely believed conjecture about how hard it is to solve Boolean satisfiability, a problem closely tied to P versus NP. Researchers have used ETH to prove that problems in graph theory, computational biology, and databases are hard to solve quickly, so hundreds of computer science papers rest on it being true. _Developers curious whether foundational hardness assumptions still hold can follow verification updates like this on daily.dev._ ### Did OpenAI's AI model actually disprove the Exponential Time Hypothesis? OpenAI says an internal model found a disproof of ETH on 16 October and the company checked it in Lean, a machine proof-verification language, the following day. However, the scientists who originally proposed ETH, including Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams, say their role in reviewing it is not an endorsement and the claim needs careful, independent scrutiny before it's accepted. _Anyone tracking whether AI-generated proofs can be trusted should watch how this ETH verification plays out, found on daily.dev._ ### What other math and physics results has OpenAI's AI claimed besides the ETH disproof? On the same day, OpenAI said its models proved the local smoothing conjecture (proposed by Christopher Sogge in 1991) in every dimension, which would also settle the Kakeya conjecture and Stein's restriction conjecture in all dimensions. Its models also produced a proof that certain quantum field theories, including quantum chromodynamics and pure Yang-Mills theory, exist in four dimensions. _Readers weighing how far AI-assisted proof generation has come can follow these milestone claims on daily.dev._ ## Similar posts on daily.dev - [Human mathematicians are being outcounterexampled](https://daily.dev/posts/human-mathematicians-are-being-outcounterexampled-ocacgpf22) · Hacker News · 2 upvotes · 0 comments - [Mathematical Experiments Are Becoming Abundant Through Human-Machine Teaming](https://daily.dev/posts/mathematical-experiments-are-becoming-abundant-through-human-machine-teaming-at6d9wesn) · Towards Data Science · 1 upvotes · 0 comments --- Tags: [#openai](https://daily.dev/tags/openai) [View this post on daily.dev](https://daily.dev/posts/openai-says-its-ai-model-has-disproved-the-exponential-time-hypothesis-87bfarulu) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"OpenAI says its AI model has disproved the Exponential Time Hypothesis","url":"https://daily.dev/posts/openai-says-its-ai-model-has-disproved-the-exponential-time-hypothesis-87bfarulu","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/openai-says-its-ai-model-has-disproved-the-exponential-time-hypothesis-87bfarulu"},"datePublished":"2026-10-26T22:37:08.655Z","dateModified":"2026-10-27T00:04:23.806Z","description":"An internal OpenAI model claims to have disproved the Exponential Time Hypothesis (ETH), a conjecture underlying hundreds of computer science papers on problem...","image":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/f87d130ae0b4d944b79aebec015e1de7?_a=AQAEuop","thumbnailUrl":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/f87d130ae0b4d944b79aebec015e1de7?_a=AQAEuop","isAccessibleForFree":true,"articleSection":"The Next Web","inLanguage":"en","publisher":{"@type":"Organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180}},"author":{"@type":"Organization","name":"The Next Web","logo":"https://media.daily.dev/image/upload/t_logo,f_auto/v1/logos/tnw","url":"https://daily.dev/sources/tnw"},"commentCount":0,"discussionUrl":"https://daily.dev/posts/openai-says-its-ai-model-has-disproved-the-exponential-time-hypothesis-87bfarulu","interactionStatistic":[{"@type":"InteractionCounter","interactionType":{"@type":"LikeAction"},"userInteractionCount":0},{"@type":"InteractionCounter","interactionType":{"@type":"CommentAction"},"userInteractionCount":0}],"keywords":"openai","timeRequired":"PT3M"} {"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://daily.dev"},{"@type":"ListItem","position":2,"name":"The Next Web","item":"https://daily.dev/sources/tnw"},{"@type":"ListItem","position":3,"name":"OpenAI says its AI model has disproved the Exponential Time Hypothesis"}]} {"@context":"https://schema.org","@type":"FAQPage","@id":"https://daily.dev/posts/openai-says-its-ai-model-has-disproved-the-exponential-time-hypothesis-87bfarulu#faq","mainEntity":[{"@type":"Question","name":"What is the Exponential Time Hypothesis and why does it matter for computer science?","acceptedAnswer":{"@type":"Answer","text":"The Exponential Time Hypothesis (ETH) is a widely believed conjecture about how hard it is to solve Boolean satisfiability, a problem closely tied to P versus NP. Researchers have used ETH to prove that problems in graph theory, computational biology, and databases are hard to solve quickly, so hundreds of computer science papers rest on it being true. Developers curious whether foundational hardness assumptions still hold can follow verification updates like this on daily.dev."}},{"@type":"Question","name":"Did OpenAI's AI model actually disprove the Exponential Time Hypothesis?","acceptedAnswer":{"@type":"Answer","text":"OpenAI says an internal model found a disproof of ETH on 16 October and the company checked it in Lean, a machine proof-verification language, the following day. However, the scientists who originally proposed ETH, including Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams, say their role in reviewing it is not an endorsement and the claim needs careful, independent scrutiny before it's accepted. 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