Tencent Hy· @TencentHunyuan · X·· 2026-07-30精选AI 评分74
AI 导读
腾讯混元借助研究智能体Hyra及Hy3模型，构造出整数集A使|A+A|与|A-A|的指数比精确达到2，解决了自1969年以来悬而未决的极值问题。此前50余年最佳构造仅略超1.1，新成果证明最优指数即为2。论文及形式化证明已公开。
推荐理由
我认为，这是AI首次真正解决一个悬而未决50年的纯数学问题，虽然定理本身小众，但它证明了AI在定理发现上的潜力，值得数学和AI交叉领域的人认真读。
正文 · 原文
For a finite set of integers (A), how much faster can (|A+A|) grow than (|A-A|)?
A 1969 theorem gave an upper bound of 2 for the exponent. For more than 50 years, the best constructions barely exceeded 1.1.
With help from our research agent Hyra and the Hy3 model, we found an explicit construction showing that the optimal exponent is exactly 2.
A 50-year-old problem, solved.
Paper: https://arxiv.org/abs/2607.27199
Hyra blog: https://hy.tencent.ai/research/hyra
Formal proof: https://github.com/linhaowei1/sum-diff-proof
来源：Tencent Hy · x.com