45年数论猜想被GPT-5.2 Pro独立完成证明，陶哲轩：没犯任何错误

Core Viewpoint - The article discusses the significant achievement of OpenAI's GPT-5.2 Pro in independently proving a mathematical conjecture known as the Erdős problem, specifically the 281st problem from the Erdős problem collection, which had remained unsolved for 45 years [2][4][5]. Group 1: Proof and Validation - The proof was verified by Fields Medalist Terence Tao, who described it as "the clearest first-class result contributed by AI to date" [3]. - The proof utilized concepts from ergodic theory and combinatorial mathematics, specifically leveraging the Birkhoff theorem and avoiding common pitfalls such as limit exchanges and quantifier order errors [9][15][12]. - Tao translated the proof into combinatorial language, confirming its validity and establishing that the proof is indeed correct [16][17]. Group 2: Alternative Solutions - An unexpected discovery was made by a user named KoishiChan, who pointed out that a simpler solution to the problem exists, utilizing two theorems established in 1936 and 1966 [18]. - The first theorem is the density convergence theorem co-proven by Harold Davenport and Paul Erdős in 1936, and the second is Rogers' theorem from a 1966 publication [19]. - This raises questions about why Erdős himself did not recognize the proximity of the solution when he proposed the problem in 1980 [20]. Group 3: AI's Success Rate and Future Implications - Following the announcement, various AI models were tested for their ability to validate the proof, with Gemini 3 Pro confirming its correctness [24]. - However, Tao cautioned that the true success rate of AI tools in solving such problems is likely skewed due to reporting biases, with only about 1% to 2% of attempts yielding positive results [30]. - Despite this low success rate, the existence of over 600 unsolved problems in the Erdős collection suggests that AI contributions could still be significant [31].