DeepMind and mathematicians use machine learning to guide new theorems in knot theory and representation theory
Davies et al. (Nature, Dec 2021) used supervised learning plus attribution to point mathematicians to hidden relationships. That led to a new theorem linking the knot signature to hyperbolic geometry, and to progress on the combinatorial invariance conjecture for Kazhdan–Lusztig polynomials.
Key facts
- Nature 600:70–74 (2021)
- Knot theory: new relation between signature and the 'natural slope' (Lackenby, Juhász); follow-up in Geometry & Topology (2024)
- Representation theory: progress towards the combinatorial invariance conjecture (Williamson)
- Humans stated and proved the theorems; ML highlighted which features mattered
Science result
- Field
- mathematics / knot theory / representation theory
- Problem
- Combinatorial invariance conjecture for Kazhdan–Lusztig polynomials; relations between knot invariants
- Result
- ML-guided discovery of a conjectured, then proved, relation between the knot signature and hyperbolic invariants, and a new approach to combinatorial invariance for symmetric groups.
- AI system
- supervised neural networks with gradient saliency
- Human role
- Human-led with AI tools: ML suggested patterns; mathematicians formulated and proved the theorems
- Verification
- Peer-reviewed in Nature; human proofs
- Status
- confirmed
What happened
DeepMind trained models to predict one mathematical quantity from others, then used attribution to show which inputs mattered, prompting expert mathematicians to formulate and prove new results.
Why it matters
It was the first Nature-level demonstration of AI contributing to pure maths research, as an intuition aid rather than a prover.
Changelog
- 2026-09-29: created
Related events
Sources (2)
- paperAdvancing mathematics by guiding human intuition with AI (Nature)
- discussionCritical review of the paper (arXiv 2112.04324)
id: 2021-12-01-deepmind-knot-theory-intuition · updated 2026-09-29 · open in the interactive timeline