OpenAI recently claimed to have solved the Navier-Stokes millennium problem, a feat qualifying for a $1 million Clay Mathematics Institute prize, but the achievement faces intense scrutiny regarding its mathematical relevance. While the company's large language model (LLM) successfully produced a "blowup" proof, critics argue the AI exploited a specific loophole within the problem's formulation. According to the original 2000 statement by Charles Fefferman, the equations allow for an optional external force, such as gravity. OpenAI’s LLM utilized a highly contrived, non-physical external force to trigger the mathematical blowup, whereas the primary challenge for mathematicians is determining if the equations blow up using only intrinsic fluid forces. Recent research by three mathematicians demonstrates that OpenAI's specific method is fundamentally incapable of being extended to the version of the problem without an external force; if the force is removed, the blowup disappears. While the LLM's result technically satisfies the Clay Institute's specific "option C" formulation, it fails to address the core physical question of whether fluid dynamics can become infinite due to its own internal properties. This controversy highlights a growing gap between LLM capabilities—which excel at constructing explicit, specific scenarios—and the ability of AI to develop the abstract new theories required to prove the impossibility of such blowups.
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