Fields Medalist Gowers pushes back on the claim that AI 'merely explores the convex hull'
burny_tech · x · 2026-10-08
Timothy Gowers questions the popular metaphor that AI "merely explores the convex hull" of existing knowledge, suggesting AI output is more like "the subgroup generated by existing mathematical knowledge" — capable of genuinely novel combinations. The debate started as a joke by @AcerFur (saying mathematicians should use "it's within the convex hull" instead of "it's trivial"), but Gowers engages seriously with what the metaphor implies about AI's ability to produce new mathematics.
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