{"id":15645,"date":"2026-10-27T15:27:18","date_gmt":"2026-10-27T14:27:18","guid":{"rendered":"https:\/\/dailyai.com\/?p=15645"},"modified":"2026-10-27T15:27:33","modified_gmt":"2026-10-27T14:27:33","slug":"openai-and-anthropic-say-ai-broke-the-same-computer-science-rule","status":"publish","type":"post","link":"https:\/\/dailyai.com\/nl\/2026\/10\/openai-and-anthropic-say-ai-broke-the-same-computer-science-rule\/","title":{"rendered":"OpenAI and Anthropic Say AI Broke the Same Computer Science Rule"},"content":{"rendered":"

Two rival AI labs say their models knocked down the same pillar of computer science, and both say it happened on the same day, 16 October. If the proofs hold, an assumption that hundreds of research papers rely on is wrong. The catch: by Anthropic’s own reckoning, the faster method would not beat plain trial and error until a puzzle has more than 10 million variables.<\/strong><\/p>\n\n\n\n

OpenAI announced the result on Monday 26 October<\/a>, alongside two other claims in mathematics and physics. A few hours later, Anthropic posted its own version<\/a> to GitHub, in a paper credited to “Claude, Anthropic”. Neither result has been independently confirmed yet. Outside experts are now checking them.<\/p>\n\n\n\n

The rule in question<\/h2>\n\n\n\n

The assumption is called the Exponential Time Hypothesis, or ETH. It is about a logic puzzle known as 3-SAT. You get a long list of conditions, each involving a few yes-or-no switches, and you have to find a setting of the switches that satisfies every condition at once.<\/p>\n\n\n\n

Checking an answer is easy. Finding one is the hard part. Each extra switch doubles the number of possible settings, so with 100 switches there are more possibilities than anyone could ever try. Computer scientists have found cleverer methods over the years, but the time needed has still grown exponentially, meaning it multiplies with every switch added.<\/p>\n\n\n\n

ETH says that will always be true: there is no shortcut that escapes that exponential growth. It has been “widely believed true since the late 1990s and a great deal of theoretical computer science was built on it being true”, MIT’s Ryan Williams told Al Jazeera<\/a>. OpenAI says the hypothesis has been used in hundreds of papers, across fields from graph theory to computational biology and databases.<\/p>\n\n\n\n

The numbers behind the claim<\/h2>\n\n\n\n

Before this month, the fastest known methods ran in about 1.328 to the power of n steps for n switches, or 1.308 to the power of n for methods that use randomness, according to Anthropic<\/span><\/span><\/span>\u2019s 49-page paper<\/a>. Both labs now say they have a method that grows more slowly than any such exponential. That is what “ETH is false” means.<\/p>\n\n\n\n

Anthropic says its result was found by an internal Claude research model that wrote 14 million output tokens, the small chunks of text a model produces, “with no human input”. Its researchers then worked with the model to improve the write-up. OpenAI says its own AI found the disproof on the same day and that it was checked in Lean, a programming language that lets a computer verify each step of a proof, the next day. OpenAI’s paper and Lean files<\/a> sit in its public GitHub repository.<\/p>\n\n\n\n

Anthropic’s paper says the two results were found “independently and concurrently” and cites OpenAI’s work. OpenAI’s announcement does not mention Anthropic, as the research-tracking site Papex points out<\/a>. Both discovery dates come from the companies themselves. The first public files appeared on 26 and 27 October.<\/p>\n\n\n\n

Why your laptop won’t notice<\/h2>\n\n\n\n

This is a result about the worst possible puzzles, at enormous sizes. Anthropic is blunt about it. Its paper says the approach seems unlikely to improve on brute force “unless n > 107<\/sup>“, or more than 10 million switches, and that “our result says nothing about solving formulas in practice.” OpenAI says turning the theory into practical gains “will require significant further research.”<\/p>\n\n\n\n

That matters because 3-SAT is not just a classroom puzzle. Programs called SAT solvers are used to check chip designs and test software, and they already handle formulas with millions of variables, because real-world cases are usually far easier than the worst case. Asked on X what developers might notice first, Williams said nobody knows yet, according to The Decoder<\/a>. Serious progress within 12 months was plausible, he said, “Or we may see nothing of the sort. I really don’t know.”<\/p>\n\n\n\n

It also does not settle the famous P versus NP question, which asks whether every problem that is quick to check is also quick to solve. Faster than exponential is still a long way from quick in that sense. Both papers say so.<\/p>\n\n\n\n

Who checks an AI’s homework<\/h2>\n\n\n\n

The checking is being led by three researchers OpenAI asked to act as “shepherds”: Russell Impagliazzo and Ramamohan Paturi of UC San Diego, two of the people who first proposed ETH, and Williams. OpenAI says they are unpaid and signed no nondisclosure agreements. At their request, OpenAI published all the raw material and agreed to fund a conference on the result.<\/p>\n\n\n\n

The three have also written an open letter making clear they are not vouching for the claim. “Our involvement should not be taken as certification of the claim,” they write, as quoted by Papex<\/a>. “If the claim is correct, it will change an important part of theoretical computer science.” They list Anthropic’s paper as a resource for the review, next to OpenAI’s.<\/p>\n\n\n\n

A Lean check is strong evidence, but not the end of the story. Lean confirms that a proof follows from the statement as it was typed in. People still have to confirm that the typed statement really says what mathematicians mean. That is the slow, human part.<\/p>\n\n\n\n

The other two claims<\/h2>\n\n\n\n

OpenAI’s announcement also claims a proof of a 1991 conjecture about how waves focus, known as local smoothing, in every dimension. Until now it was proved only in two dimensions, in 2019. OpenAI says the result also settles two other well-known problems, the Kakeya and Stein restriction conjectures. That proof and its Lean files are public.<\/p>\n\n\n\n

The third claim is in physics. OpenAI says its models proved that certain theories of how particles interact, including quantum chromodynamics, which describes the force holding atomic nuclei together, exist on solid mathematical ground. That includes part of one of the seven Millennium Prize Problems, which each carry a $1 million award. OpenAI says it solved only the existence part, not the “mass gap” half, so the prize problem stays open. A group led by Nobel laureate David Gross is reviewing that work, and the material has not been released in full<\/a>.<\/p>\n\n\n\n

That last choice has drawn criticism. The Advisory Group on Mathematics and Artificial Intelligence<\/a>, a panel of mathematicians hosted at the Institute for Advanced Study, called on OpenAI on 26 October to release the physics outputs “without delay”. It argues that OpenAI said it was waiting for the Lean check, and “by their own account this is now complete.”<\/p>\n\n\n\n

De eenvoudige lezing<\/h2>\n\n\n\n

Two companies claiming the same breakthrough on the same day is new. It suggests the leading AI models can now find results that experts spent decades failing to find, and that more than one lab can do it. It also shows how unready science is for this. There is no shared clock for who found what first, and no agreed rule for when an AI-made proof counts as checked.<\/p>\n\n\n\n

For now, the honest score is: three big claims, zero independent confirmations. The examiners say they will share findings as they go. Until they report, ETH is best described as claimed false, not proved false.<\/p>","protected":false},"excerpt":{"rendered":"

Both labs say their AI models disproved the Exponential Time Hypothesis on the same day, 16 October. Outside experts are now checking, and Anthropic says the gain only shows up beyond 10 million variables.<\/p>","protected":false},"author":16,"featured_media":15646,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-15645","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry"],"yoast_head":"\nOpenAI and Anthropic Say AI Disproved a Core Computing Rule<\/title>\n<meta name=\"description\" content=\"OpenAI and Anthropic both say AI disproved the Exponential Time Hypothesis on 16 October. 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