Top mathematicians debate: is AI exploration a convex hull or a generated subgroup?
gleech · x · 2026-10-08
- Abel laureate Timothy Gowers pushes back on the popular metaphor that AI "merely explores the convex hull" of existing math, suggesting the subgroup generated by existing knowledge may be a better analogy, since combinations of known techniques can exceed the hull.
- Elliot Glazer replies that the truth lies between the two, but closer to the hull: unbounded application of existing techniques would certainly contain every ZFC-derivable theorem.
- The exchange speaks to whether AI can produce genuinely original mathematical results.
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