New ArXiv Papers on Grothendieck Constant via Human-AI Collaboration
Published:
I’m excited to share two new papers on arXiv that present breakthrough results on the Grothendieck constant through human-AI mathematical collaboration.
The first paper, New Lower and Upper Bounds for the Grothendieck Constant, tightens the best known bounds on $K_G$ to
\[\frac{6\pi}{11} \leq K_G \leq \frac{\pi}{2 \log(1 + \sqrt{2})} - 10^{-4},\]which together pin down the previously unknown tenths digit of $K_G$ to be 7. The lower bound comes from establishing limitations on asymptotically optimal Krivine schemes rather than constructing explicit gap instances, and the upper bound from the first asymptotic construction of rounding schemes, where previous work considered only low-dimensional schemes.
The second paper, Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human–AI Mathematical Collaboration, is a detailed account of how we actually got there. It describes the long-horizon AI research system we engineered, where it was strong and where it was weak, and what conditions made it possible for the system to arrive at insights that domain experts considered novel.
The two papers are companions: one presents and proves the mathematical results, the other documents the human–AI research process behind them.