---
id: "2021-12-01-deepmind-knot-theory-intuition"
url: "https://postcutoff.com/e/2021-12-01-deepmind-knot-theory-intuition/"
as_of: "2026-11-13T13:49:00+01:00"
date: "2021-12-01"
date_precision: day
category: science
importance: 3
confidence: high
status: [Result confirmed]
verification: Peer-reviewed
sources: 2
editor: human editor
human_review: null
version: "2026-10-04"
---

As of: 2026-11-13 13:49 CET.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/e/2021-12-01-deepmind-knot-theory-intuition/

# 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

## 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.

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): in its training data
- Claude Opus 5.5 (training cutoff June 2026): in its training data
- Gemini 4 Hydrogen (training cutoff March 2026): in its training data
- Grok 4.7 (training cutoff May 2026): in its training data

## Sources

1. [Advancing mathematics by guiding human intuition with AI (Nature)](https://www.nature.com/articles/s41586-021-04086-x) (nature.com, paper)
2. [Critical review of the paper (arXiv 2112.04324)](https://arxiv.org/abs/2112.04324) (arxiv.org, discussion)

## Changes

- 2026-09-29 (filed): Created

## Related

- 2023-12-14: [FunSearch: an LLM finds new cap-set constructions, the first LLM discovery in open maths](https://postcutoff.com/e/2023-12-14-funsearch-cap-sets/index.md)