What sort of maths are LLMs good at?
Summary
In this post, mathematician Timothy Gowers examines what kinds of mathematics current LLMs are particularly good at, prompted by their recent success in solving major open problems. He argues that although LLMs can prove difficult theorems, their most striking achievements often involve finding examples or counterexamples, because their enormous mathematical knowledge and ability to explore many possible approaches rapidly make them well suited to trial-and-error and probabilistic search.
However, humans may still have an advantage in problems requiring deep conceptual insight and the ability to “prune” an enormous search tree, recognizing which approaches are genuinely promising rather than repeatedly pursuing plausible but unproductive ideas. Gowers emphasizes that this distinction is temporary rather than fundamental: LLMs are improving rapidly and may soon develop this mathematical “nose” themselves, potentially transforming mathematical discovery.
ARTICLE / ARCHIVE
Summary
In this post, mathematician Timothy Gowers examines what kinds of mathematics current LLMs are particularly good at, prompted by their recent success in solving major open problems. He argues that although LLMs can prove difficult theorems, their most striking achievements often involve finding examples or counterexamples, because their enormous mathematical knowledge and ability to explore many possible approaches rapidly make them well suited to trial-and-error and probabilistic search.
However, humans may still have an advantage in problems requiring deep conceptual insight and the ability to “prune” an enormous search tree, recognizing which approaches are genuinely promising rather than repeatedly pursuing plausible but unproductive ideas. Gowers emphasizes that this distinction is temporary rather than fundamental: LLMs are improving rapidly and may soon develop this mathematical “nose” themselves, potentially transforming mathematical discovery.
ARTICLE / ARCHIVE
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