Mathematicians debate two metaphors for how LLMs do math: interpolation vs. recombination
Afinetheorem · x · 2026-10-08
A notable math-Twitter exchange on LLM creativity: Timothy Gowers pushes back on the popular idea that AI "merely explores the convex hull" of existing knowledge, suggesting a better metaphor might be the subgroup generated by existing mathematical knowledge.
The resharing author distills two useful visualizations: the LLM as finding points by interpolating between existing ones (new ideas live between existing ones), or as recombining existing results through arbitrarily long iterated operations. The two framings imply different ceilings for AI-driven mathematical discovery.
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