OpenAI Proves a Number Theory Problem; Related Progress May Offer Clues for P≠NP Research
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Author:小编   

Recently, an internal model at OpenAI claimed to have proven the nonexistence of Landau-Siegel zeros—a problem in analytic number theory that had remained unresolved for decades. The original proof was only eight pages long and was later compressed to five pages by several leading mathematicians. The nature of this result—"extremely difficult to find, extremely easy to verify"—has sparked intense discussion in academia about P vs. NP, a core problem in computer science. OpenAI subsequently released hundreds of mathematics manuscripts, achieving breakthroughs in core peripheral directions related to P vs. NP, such as depth-3 circuit lower bounds, proof of the unique games conjecture, and complete derandomization of randomized logarithmic space. There were even instances of human mathematicians rushing to publish results before AI releases. However, academic experts have generally remained calm, pointing out that current AI results still have hard flaws, including incomplete verification, poor readability, and gaps in key routes such as lower bounds for general Boolean circuits—and that AI has not yet truly touched the P vs. NP problem itself. At present, academia is divided on where this problem is heading, and some views hold that AI expending massive computational power to search for proofs while humans need only a short time to verify the results is itself a vivid illustration of P≠NP.