王虹与三维挂谷猜想：深度解析基础数学的AI能力边界

TL;DR - A commentary piece using Wang Hong and Joshua Zahl's 127-page proof of the three-dimensional Kakeya (挂谷) conjecture as a case study for where current AI hits its ceiling in frontier mathematics. It argues AI is an "outstanding student" — great at delegated technical subtasks — but not yet a "master" capable of paradigm-creating research.

• The 3D Kakeya problem is framed as qualitatively harder than the 2D case: rigid rather than flexible geometry, infinitely nested multi-scale/chaotic structure, "sticky" Kakeya configurations, and the limits of existing Fourier/harmonic analysis tooling.
• Wang and Zahl's contribution is described as system-level innovation — abandoning prior research paths and building new machinery — rather than incremental application of known techniques.
• Four stated AI limitations: reuse of existing paradigms instead of inventing new frameworks; no global research strategy judgment; inability to sustain very long, multi-layer, cross-domain logical chains (a 127-page proof spanning four branches of math); and no mathematical intuition for structures with no precedent or template.
• Conclusion positions AI as an accelerator for verification, gap-hunting, symbolic simplification, and pruning dead-end approaches, dominant on competition-style bounded problems, while century-old conjectures remain human territory.
• Note: the piece is opinion/analysis reposted via a WeChat account (数据派THU), not a technical report; no benchmarks or AI experiments are presented.