Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration
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TL;DR - A case study documenting how an AI research system was used over a long horizon to tighten the best known bounds on the Grothendieck constant $K_G$, alongside a candid account of what worked and what didn't in human-AI mathematical collaboration.
- Reports improved bounds of $6\pi/11 \le K_G \le \pi/(2\log(1+\sqrt{2})) - 10^{-4}$, where $K_G$ quantifies the gap between combinatorial problems and their continuous (SDP) relaxations; the exact value remains unknown.
- The AI system produced insights that domain experts judged genuinely novel, rather than merely mechanizing known arguments.
- The paper's main contribution is methodological: a detailed discussion of the AI's strengths and weaknesses on long-horizon research tasks.
- Emphasizes constructing "ideal conditions" — problem framing and workflow setup — as a prerequisite for AI-driven breakthrough insights.
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Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration
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TL;DR - A case study documenting how an AI research system was used over a long horizon to tighten the best known bounds on the Grothendieck constant $K_G$, alongside a candid account of what worked and what didn't in human-AI mathematical collaboration.
- Reports improved bounds of $6\pi/11 \le K_G \le \pi/(2\log(1+\sqrt{2})) - 10^{-4}$, where $K_G$ quantifies the gap between combinatorial problems and their continuous (SDP) relaxations; the exact value remains unknown.
- The AI system produced insights that domain experts judged genuinely novel, rather than merely mechanizing known arguments.
- The paper's main contribution is methodological: a detailed discussion of the AI's strengths and weaknesses on long-horizon research tasks.
- Emphasizes constructing "ideal conditions" — problem framing and workflow setup — as a prerequisite for AI-driven breakthrough insights.