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Earlier this month, OpenAI announced that it had found a solution for one of the biggest unsolved problems in math, the Navier-Stokes equations, by directing 10,000 of its powerful AI agents to work on the enigma for 88 hours straight. It was an occasion fraught with controversy<\/a>, however, as mathematicians accused the company of essentially stealing their work.<\/p>\n That controversy is still rippling through the math world. But what has the AI\u2019s solution taught us? Not a lot, as it turns out, because the proof it wrote, while technically correct, is borderline incomprehensible.<\/p>\n \u201cSo far it\u2019s been very difficult to really extract any human understanding from this new AI proof,\u201d James Maynard, an Oxford mathematician, told NPR<\/a>.<\/p>\n \u201cThe paper is not written for humans,\u201d echoed Javier\u00a0G\u00f3mez-Serrano, a mathematician at Brown University who uses AI in his own research. The AI\u2019s proof could help the field after \u201csome serious re-writing,\u201d he added, but \u201cas of today, the paper doesn\u2019t teach us much.\u201d<\/p>\n The Navier-Stokes equations mathematically describe how fluids, ranging from a rush of wind to the churn of ocean currents, move and behave. They\u2019ve been used for nearly two centuries with reliable results, but why they work remains something of a mystery. Scientists have been eager to push the equations to their limits and see if their predictions could reach a breaking point where they describe a scenario that makes no sense in the real world. Reifying the equation\u2019s importance, the Clay Mathematics Institute in 2000 listed the Navier-Stokes as one of its six Millennium Problems, with the prize for solving it at $1 million.<\/p>\n OpenAI claimed that its swarm of AI agents identified a scenario in which the fluids accelerate to an infinite velocity, creating a \u201cblow up\u201d or singularity \u2014 something, of course, that\u2019s impossible in the physical universe.<\/p>\n Hours before the announcement, NYU mathematician Tristan Buckmaster, who had been working on the Navier-Stokes problem for years, accused OpenAI of jumping on his work without notice or permission, and thereby essentially pilfering his ideas by pushing them over the finish line. He claimed that OpenAI\u2019s work followed a similar path to his own, which he says that no one else in the field was pursuing. Because he\u2019d been using OpenAI\u2019s Codex tool to help with his research<\/a>, he insinuated, OpenAI may have secretly accessed his notes. When he approached OpenAI about this, he claims that the company said it would credit him on its paper if he dropped his collaborator, Levent Alp\u00f6ge, who was working at Anthropic.\u00a0<\/p>\n OpenAI denied the allegations but admitted that it \u201ccannot rule out that de-identified data derived from their usage of our products helped improve our models.\u201d<\/p>\n There\u2019s also some groaning about the Navier-Stokes problem OpenAI says it solved. To earn the Clay Institute\u2019s Millennium prize, mathematicians could solve either the \u201cforced\u201d or \u201cunforced\u201d version of the problem. The forced version involved an external force like gravity applied to the fluids. As laid out in a recent Scientific American piece<\/a>, experts are chiefly interested in finding a purer scenario where the equations \u201cblow up\u201d without an external force and only with the forces within the fluid. OpenAI\u2019s solution, however, relies on an external force. More than that, a recent proof<\/a> posted by mathematicians contends that OpenAI\u2019s solution can never lead to solving the full problem.<\/p>\n \u201cThe most important problem is unsolved,\u201d Luis Silvestre, a mathematician at the University of Chicago, told SciAm. \u201cThe Clay problem is settled, but the main problem for the Navier-Stokes equations is not.\u201d<\/p>\n Still, mathematicians are in agreement that, however technical it may be, OpenAI\u2019s solutions are valid, even if it\u2019ll take many more weeks to unpack the AI\u2019s ramblings.<\/p>\n