{"id":623104,"date":"2026-09-21T18:32:14","date_gmt":"2026-09-21T18:32:14","guid":{"rendered":"https:\/\/www.newsbeep.com\/il\/623104\/"},"modified":"2026-09-21T18:32:14","modified_gmt":"2026-09-21T18:32:14","slug":"did-openai-solve-the-wrong-navier-stokes-problem","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/il\/623104\/","title":{"rendered":"Did OpenAI solve the wrong Navier-Stokes problem?"},"content":{"rendered":"

Two weeks ago OpenAI claimed a solution<\/a> to one of the biggest open problems in math<\/a>\u2014the Navier-Stokes problem<\/a>\u2014an achievement worth a $1-million prize from the Clay Mathematics Institute. The proof ignited a powder keg<\/a> of concern over artificial intelligence companies\u2019 race to disrupt<\/a> the subject.<\/p>\n

But with the dust still far from settled, a different controversy is emerging: Did OpenAI even solve the right Navier-Stokes problem?<\/p>\n

Generated by an internal large language model (LLM), OpenAI\u2019s proof relies on an approach that many experts find unnatural. It solves a variant of the problem that mathematicians say is disconnected from reality and thus less interesting. In a sense, the LLM found and exploited a loophole in the framing of the question.<\/p>\n

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\u201cThe most important problem is unsolved,\u201d says Luis Silvestre, a mathematician at the University of Chicago. \u201cThe Clay problem is settled, but the main problem for the Navier-Stokes equations is not.\u201d<\/p>\n

Furthermore, last Thursday, three mathematicians posted a proof of their own<\/a> that showed that OpenAI\u2019s method can never be extended to solve the full problem. In other words, the loophole will never be closed, barring some completely new idea.<\/p>\n

The Navier-Stokes equations are supposed to describe how fluids flow, but mathematicians doubt whether they can always be trusted. The million-dollar problem is about whether the equations ever \u201cblow up,\u201d which would mean they\u2019d allow the flow to be infinitely fast at points\u2014something that can\u2019t happen in the real world.<\/p>\n

But there\u2019s one piece of the equations that\u2019s optional\u2014sometimes it\u2019s there; sometimes it isn\u2019t. The \u201cit\u201d here is an external force such as gravity that affects how a fluid moves. \u201cAll fluids we know of are under some kind of external force,\u201d says mathematician Diego C\u00f3rdoba. \u201cSo to have the force makes complete sense.\u201d<\/p>\n

When most experts think about the Navier-Stokes problem, though, it\u2019s without this force. They want to find a purer, more fundamental way for the equations to blow up by using only the intrinsic forces within any fluid\u2014not by applying some specific, precisely contrived external force. \u201cMost of the other groups, it\u2019s true, were specifically considering the scenario without a force,\u201d says mathematician Luis Mart\u00ednez-Zoroa.<\/p>\n

In the past few years, though, C\u00f3rdoba and Mart\u00ednez-Zoroa put all their focus on this niche piece of the equations and laid out a method to build a very specific external force to trigger a blowup. On September 7 two other mathematicians used their program (and AI) to produce a blowup for a frictionless fluid\u2014considered a major step toward blowing up Navier-Stokes. OpenAI finished the job less than a day later\u2014timing that has led to a heated dispute between the latter two mathematicians and the company.<\/p>\n

But the new work released last Thursday shows unequivocally that if the force is removed, the blowup will disappear. OpenAI\u2019s method can never work, in fact, without using a very contrived equation for the force that is unlike anything that could occur in the real world. \u201cThey essentially prove that the formulation with an external force was different from the problem we really wanted to solve,\u201d Silvestre says.<\/p>\n

In other words, the LLM\u2019s result does not\u2014and will never\u2014answer the Navier-Stokes problem that mathematicians really care about.<\/p>\n

It did, however, unambiguously solve the problem according to the Clay Institute\u2019s original formulation. The official problem statement<\/a>, penned in 2000 by mathematician Charles Fefferman, offers an option called \u201cC,\u201d in which solutions are allowed to use an external force like OpenAI\u2019s.<\/p>\n

Now fluid dynamicists are grappling with a possibility few had considered before: the idea that the Navier-Stokes equations can blow up but only with an external force. In this scenario, you can mathematically place a fluid in a specific, unrealistic situation to break the equations, yet the blowup can never come from the fluid itself.<\/p>\n

\u201cIt\u2019s really uncertain at this moment,\u201d says mathematician Gonzalo Cao-Labora. \u201cDepending on the answer to this, I think the contribution of OpenAI will be regarded differently.\u201d If it turns out to be true, he adds, \u201cpeople would probably think about the Clay problem and say, \u2018We shouldn\u2019t have put the external force in the statement.\u2019\u201d<\/p>\n

This might even be good news for \u201cteam humanity.\u201d LLMs are great at finding blowups that exist\u2014at searching the infinite landscape of fluid scenarios and plucking out the precise situation that breaks the equations. But proving that blow-up is impossible is a kind of math AI still struggles with. \u201cWe may be at less of a disadvantage, or maybe an advantage, compared to LLMs,\u201d says Cao-Labora. \u201cLLMs are especially good at constructing things that are very explicit and not as good\u2014for now\u2014in making new theory.\u201d<\/p>\n

But regardless of whether the path to solving the full Navier-Stokes problem requires a clever new blowup or a whole new mathematical discipline, everyone is becoming more hesitant to bet against the machines.<\/p>\n

\u201cWe are really amazed with how [the technology] has evolved in the last year\u2014so we don’t know how it will look in one year,\u201d says Cao-Labora. \u201cIt\u2019s really a wake-up call to the community.\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"Two weeks ago OpenAI claimed a solution to one of the biggest open problems in math\u2014the Navier-Stokes problem\u2014an…\n","protected":false},"author":2,"featured_media":623105,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[345,343,344,85,46,125],"class_list":["post-623104","post","type-post","status-publish","format-standard","has-post-thumbnail","category-artificial-intelligence","tag-ai","tag-artificial-intelligence","tag-artificialintelligence","tag-il","tag-israel","tag-technology"],"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/posts\/623104","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/comments?post=623104"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/posts\/623104\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/media\/623105"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/media?parent=623104"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/categories?post=623104"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/il\/wp-json\/wp\/v2\/tags?post=623104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}