On 1 December 2021 DeepMind, working with mathematicians at Oxford and the University of Sydney, published in Nature the first widely recognized cases of machine learning contributing to discoveries in pure mathematics. Rather than having an AI prove theorems on its own, the team used models to detect patterns in mathematical data and point human researchers toward relationships worth investigating.
In knot theory, working with Marc Lackenby and Andras Juhasz, the collaboration found a previously unknown connection between a knot’s algebraic signature and its geometry, formalized through a new quantity they called the natural slope, leading to a proven theorem. In representation theory, working with Geordie Williamson, the approach produced insight and a candidate algorithm bearing on the combinatorial invariance conjecture, an open problem of roughly four decades, which Williamson then advanced and checked across millions of examples.
This milestone is significant because it showed AI could play a real role at the frontier of theoretical mathematics, a domain long thought to depend on uniquely human creativity. The pattern it established, with the machine guiding human intuition rather than replacing it, foreshadowed the more autonomous mathematical systems such as AlphaGeometry and AlphaProof that DeepMind would build over the next three years.