Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration

Excerpt

arXiv:2608.11195v3 Announce Type: replace Abstract: 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{6\pi}{