Packing a Punch: How Model‑Based AI Outperformed Decades of Sphere‑Packing Theory
Opening — Why this matters now AI’s recent victories in mathematics—AlphaGeometry, DeepSeek‑Prover, AlphaEvolve—have leaned on a familiar formula: overwhelming compute, evolutionary thrashing, and enough sampling to make Monte Carlo blush. Effective, yes. Elegant? Hardly. Sphere packing, however, does not care for this style of progress. Each evaluation in the three‑point SDP framework can require days, not milliseconds. There is no room for “just try another million candidates.” Any system operating here must think, not flail. ...