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 - OpenAI's latest model, GPT-5.2 Pro, has independently proven a conjecture from the Erdős problem set, marking a significant achievement in AI's capability in mathematical reasoning [1][2]. Group 1: The Proof and Its Validation - The conjecture, known as the 281st problem in the Erdős problem library, was proposed in 1980 and remained unsolved for 45 years until a researcher named Neel Somani presented it to GPT-5.2 Pro [2]. - The proof utilized the infinite Adele integer ring and involved the Haar measure and pointwise ergodic theorem, transitioning from pointwise convergence to uniform convergence [3]. - The proof has been validated by Fields Medalist Terence Tao, who noted that GPT-5.2 Pro did not make common errors typically seen in previous AI models, such as mistakes in limit exchanges or quantifier order [8]. Group 2: Alternative Solutions and Historical Context - An unexpected discovery revealed that the problem has a simpler solution using two theorems established in 1936 and 1966, namely the density convergence theorem and Rogers' theorem [9]. - Terence Tao communicated with mathematician Tenenbaum, who confirmed that the problem could be solved using these classical results, suggesting that the problem's statement might have been altered at some point [10]. Group 3: AI's Performance and Statistical Insights - Following the announcement, various AI models were tested for cross-validation, with Gemini 3 Pro confirming the proof's validity [11]. - However, Tao cautioned that the true success rate of AI in solving mathematical problems is likely skewed due to reporting bias, as negative results are less likely to be shared [11]. - Current data indicates that AI tools have a real success rate of approximately 1% to 2% on Erdős problems, which, despite being low, still represents a significant number of non-trivial contributions given the existence of over 600 unsolved problems in the library [12].