机器之心·2026-02-03 14:22Core Insights - Google has made significant progress with its Gemini model, successfully addressing 13 problems from the Erdős Problems database, including 5 novel solutions and 8 rediscoveries of existing answers [1][2][4]. Research Overview - The Erdős Problems database, named after mathematician Paul Erdős, contains 1,179 problems, with 483 (41%) classified as solved. However, many "open" problems may have existing solutions that were not previously identified [4][5]. - The research utilized a custom AI agent named Aletheia, which employed a natural language verifier to filter approximately 700 open Erdős problems down to 212 potential solutions [9]. Methodology - Aletheia's process involved initial filtering by non-expert mathematicians, reducing candidates to 27, which were then rigorously reviewed by domain experts. Out of about 200 candidates, 137 (68.5%) had fundamental errors, while only 13 (6.5%) provided meaningful answers to Erdős's original questions [9][12]. Key Results - The 13 meaningful solutions were categorized into four types: 1. Autonomous solutions (Erdős-652, Erdős-1051) where Aletheia found the first correct solution, although Erdős-652 was based on existing literature [14]. 2. Partial AI solutions for multi-part problems (Erdős-654, Erdős-935, Erdős-1040) [15]. 3. Independent rediscoveries (Erdős-397, Erdős-659, Erdős-1089) where solutions were already known but not initially recognized [15]. 4. Literature identification (Erdős-333, Erdős-591, Erdős-705, Erdős-992, Erdős-1105) where existing solutions were identified despite being marked as open [15][16]. Research Significance - The findings indicate that AI has reached a level where it can tackle "low-hanging fruit" in mathematical problems, providing a new benchmark for AI research in mathematics. However, the authors caution against overstating the mathematical significance of these results, as they are solvable by any expert in the field [19]. - The study highlights challenges in verifying the originality of solutions and the potential for "unconscious plagiarism" where AI reproduces knowledge from training data without proper citation [19][20].