半世纪难题48小时破解！陶哲轩组队把AI数学玩成打怪游戏了

Core Viewpoint - The collaboration between mathematicians and AI has led to the resolution of the long-standing Erdős 1026 problem, which had remained unsolved for 50 years, in just 48 hours [1][2][3]. Group 1: Problem Overview - The Erdős 1026 problem was proposed in 1975 and involves determining the minimum possible value of a function related to a game theory scenario involving two players, Alice and Bob [8][10][12]. - The problem's complexity was highlighted by the introduction of a maximum constant c(n) that represents the minimum proportion of coins Bob can guarantee to take, regardless of how Alice distributes them [10][13]. Group 2: AI's Role in the Solution - AI tools played a crucial role in solving the problem quickly, with traditional methods potentially taking weeks or months to reach a conclusion [3][5]. - The use of AI models, such as Harmonic and AlphaEvolve, allowed mathematicians to automate the construction and proof of key inequalities, transforming the original problem into a computational geometry challenge [16][18][22]. Group 3: Collaborative Efforts - The solution involved multiple mathematicians working together, with contributions from Boris Alexeev, Koishi Chan, and Lawrence Wu, showcasing the effectiveness of human-AI collaboration [17][28][32]. - The collaborative approach of combining human insight with AI capabilities is emerging as a new trend in mathematical problem-solving [46]. Group 4: Historical Context and Future Implications - The Erdős problems, proposed by the renowned mathematician Paul Erdős, have been a significant part of mathematical research, with many remaining unsolved [39][41]. - The increasing success of AI in solving these problems suggests a shift in how mathematical research may be conducted in the future, with AI becoming a standard tool for researchers [41][42].