ChatGPT 5.5 Pro与Claude Fable协作破解公平分配难题
I just had a fascinating call with Eyad Alkassar (@AlkassarEyad) about how ChatG…
展示了ChatGPT 5.5 Pro与Claude在复杂数学证明中的具体分工与协作细节，是AI Agent科研能力的标杆案例，值得模型开发者关注其推理与验证能力。
I just had a fascinating call with Eyad Alkassar (@AlkassarEyad) about how ChatGPT 5.5 Pro helped move the frontier of an open problem in computer science.
我刚和 Eyad Alkassar (@AlkassarEyad) 进行了一次引人入胜的通话，讨论了 ChatGPT 5.5 Pro 如何推动计算机科学中一个开放问题的前沿进展。
The problem sounds abstract, but it is surprisingly intuitive:
这个问题听起来很抽象，但出奇地直观：
Imagine four people dividing nine objects. Each person may value them differently. The goal is to find a division so fair that, after any single object is removed from someone else’s pile, nobody would prefer what remains to their own pile.
想象四个人分配九个物品。每个人对这些物品的估值可能不同。目标是找到一种分配方式，使得公平到即使从别人的堆中移除任意一个物品后，也没有人会觉得剩下的比自己的堆更好。
This criterion is called envy-freeness up to any good, or EFX.
这个标准被称为“对任何物品都无嫉妒”（Envy-Freeness up to Any Good），简称 EFX。
Whether complete EFX allocations always exist for four or more people remains open. For four people, the previous general guarantee stopped at seven objects.
对于四人或更多人，完全 EFX 分配是否总是存在仍然是一个未解之谜。对于四人情况，之前的通用保证最多只覆盖到七个物品。
A new preprint by Eyad Alkassar, Mahmoud Fouz and renowned computer scientist Kurt Mehlhorn now presents a proof for up to nine.
Eyad Alkassar、Mahmoud Fouz 和著名计算机科学家 Kurt Mehlhorn 的一篇新预印本现在提出了最多九个物品的证明。
The story behind it is remarkable.
其背后的故事非同寻常。
Over dinner, Eyad challenged Mehlhorn to give AI one of the harder open problems in his field. Eyad and Mahmoud are both computer science PhDs who had spent years building startups and were newcomers to fair division. They built a research workflow around several AI systems.
在一次晚餐中，Eyad 挑战 Mehlhorn 让 AI 解决他领域内较难的开放问题之一。Eyad 和 Mahmoud 都是计算机科学博士，曾花费多年时间创业，是公平分配领域的新手。他们围绕多个 AI 系统构建了一个研究工作流。
At one point, Fable had questions about one of Mehlhorn’s papers and repeatedly urged Eyad to contact him. After Eyad refused twice, the AI pointed out that they were only around 30 kilometers apart and suggested that a short drive would be worth it.
有一次，Fable 对 Mehlhorn 的一篇论文有疑问，并反复敦促 Eyad 联系他。在 Eyad 两次拒绝后，AI 指出他们相距仅约 30 公里，并建议短途开车一趟是值得的。
According to Eyad, the situation became even stranger once the proof was finished. Fable then advised him against sending the result to Mehlhorn, warning that he might be a competitor and that an incorrect proof could be embarrassing.
据 Eyad 称，一旦证明完成，情况变得更加奇怪。随后 Fable 建议他不要将结果发送给 Mehlhorn，警告说对方可能是竞争对手，而错误的证明可能会令人尴尬。
Eyad contacted him anyway.
Eyad 还是联系了他。
Mehlhorn reviewed and verified the proof architecture, refined the arguments and joined the paper as a co-author.
Mehlhorn 审查并验证了证明架构，完善了论证，并作为共同作者加入了该论文。
According to the paper, Claude Fable performed the analysis and lemma proofs, authored the trusted verification layer and audited its soundness. ChatGPT 5.5 Pro proposed most of the candidate attacks and optimizations.
根据论文，Claude Fable 执行了分析和引理证明，撰写了可信验证层并审计了其正确性。ChatGPT 5.5 Pro 提出了大多数候选攻击和优化方案。
Eyad and Mahmoud selected the systems, assigned their roles, coordinated their communication and provided the computing infrastructure.
Eyad 和 Mahmoud 选择了这些系统，分配了它们的角色，协调了它们之间的通信，并提供了计算基础设施。
The proof divided the space into 36,152 canonical cases after symmetry reduction. The closing run verified all 122,553 certificates using Z3 and completed 141,878,161 per-clause soundness checks with zero reported failures.
经过对称性归约后，证明将空间划分为 36,152 个规范案例。最后的运行使用 Z3 验证了所有 122,553 个证书，并完成了 141,878,161 次子句级正确性检查，报告零失败。
The general theorem for an unlimited number of goods remains open. This result moves the known frontier from seven goods to nine.
关于无限数量物品的通用定理仍然是开放的。这一成果将已知的边界从七个物品推进到了九个。
The authors describe the process as “AI led, human assisted and verified.”
作者将这一过程描述为“AI主导、人类辅助与验证。”
For me, this is one of the clearest examples yet of current AI systems contributing substantial work to a new mathematical proof.
在我看来，这是迄今为止当前AI系统为新数学证明贡献大量工作的最清晰案例之一。
I found the story too remarkable not to share.
我觉得这个故事太非凡了，不分享说不过去。
Paper: https://arxiv.org/abs/2608.08590
论文：https://arxiv.org/abs/2608.08590
更进一步：量化金融体系
看懂新闻只是起点——沿量化金融路径，把它变成能交付的工程能力