想知道AI怎么帮数学家干活？这篇论文用Grothendieck常数当例子，讲AI怎么把已知界限又收紧了一截，还聊了AI的强项和翻车点，挺实在的。
arXiv论文展示了AI在数学研究中改进Grothendieck常数K_G界限的案例。研究者将K_G的已知界限收紧至6π/11 ≤ K_G ≤ π/(2log(1+√2)) - 10^-4。AI系统提出了领域专家认为新颖的见解。论文详细讨论了AI在数学研究中的优缺点，以及创造理想条件让AI产生突破性见解的经验。
Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration
AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively. Towards this, we present an extensive case study of how AI was used to improve bounds on the Grothendieck constant $K_G$, which captures the hardness between combinatorial problems and their continuous relaxations. Specifically, while the precise value of $K_G$ is not known, we recently tightened the best known bounds to \[ \frac{6π}{11} \;\le\; K_G \;\le\; \fracπ{2\log(1+\sqrt2)} - 10^{-4}. \] Crucially, these improvements were achieved using an AI research system that could arrive at insights deemed novel by domain experts. We give a detailed discussion of our experience using AI for mathematics research, particularly touching upon its strengths and weaknesses, as well as our experience with creating ideal conditions for AI to arrive at breakthrough insights.