Core Insights - The article discusses the resolution of the Erdős problem 339, a significant mathematical challenge that was previously marked as unsolved but was actually resolved in 2003. This was discovered using GPT-5 Pro, which identified the relevant literature through an image of the problem [1][5][7]. Group 1: Erdős Problem 339 - Erdős problem 339 is a classic problem in number theory concerning the existence of a positive lower density for the set of integers that can be expressed as the sum of exactly r distinct elements from a given r-ary basis [2][3]. - The problem was previously thought to be unresolved, but it was confirmed that it had been solved in a paper published in the Journal für die reine und angewandte Mathematik in 2003 [5][6]. Group 2: Community Response - The discovery made by GPT-5 Pro sparked significant interest and discussion among mathematicians and online communities, highlighting the tool's capability in identifying existing solutions to complex problems [1][4][17]. - Various mathematicians engaged in discussions about the implications of the Erdős problem and its connections to other mathematical conjectures, such as Waring's Problem, emphasizing the rigorous conditions of the Erdős problem compared to other cases [3][4]. Group 3: Implications of GPT-5 Pro - The use of GPT-5 Pro in academic research has been praised for its efficiency in identifying flaws in published papers, demonstrating its potential to accelerate the verification of scientific literature [17][18][21]. - Suggestions for optimizing the use of GPT-5 Pro in research include deep reading techniques and circularity audits, which could enhance the process of reviewing scientific documents [21].

西风 发自 凹非寺 量子位 | 公众号 QbitAI 人类遗忘的难题解法，被GPT-5 Pro重新找出来了！ 这事儿聚焦于 埃 尔德 什 问 题 #339 ，这是著名数学家 保罗・埃 尔德 什 提出或转述的近千道问题之一，收录于erdosproblems.com网 站。该网站记录了每道题目的当前状态，其中约三分之一已解决，大部分仍待解。 尤其值得关注的是，GPT-5 Pro仅通过埃尔德什问题 #339的图片 ，直接定位到了关键文献。 此前该问题被标为处于"未解决"状态 ，属于待攻克的数学难题，不少人还在继续研究探讨。 直到最近，有人用GPT-5 Pro检索后才发现，该问题 实 际在 2003年就 已被解决了 。 OpenAI研究员Sebastien Bubeck将此事分享出来后立马引发大量网友关注。 By the way，陶哲轩的著名成果之一，就是通过"遍历理论 （ergodic theory ） "工具，突破了"埃尔德什差异问题"这一困扰数学界几十年的 猜想。 问题详情 具体来看，埃尔德什问题 #339是数论中加法基方向的一个经典问题 ，表述为： 设A⊆N是一个r阶基（即每个足够大的整数都能表示为A中r个元 ...