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Cited by 451

The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.

Advancing mathematics by guiding human intuition with AI

Open access
Davies, Alex, Veličković, Petar, Buesing, Lars, Blackwell, Sam, Zheng, Daniel, Tomašev, Nenad, Tanburn, Richard, Battaglia, Peter, Blundell, Charles, Juhász, András, Lackenby, Marc, Williamson, Geordie, Hassabis, Demis, Kohli, Pushmeet·2021·Nature
DOI 10.1038/s41586-021-04086-x
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Abstract

The practice of mathematics involves discovering patterns and using these to formulate and prove conjectures, resulting in theorems. Since the 1960s, mathematicians have used computers to assist in the discovery of patterns and formulation of conjectures 1, most famously in the Birch and Swinnerton-Dyer conjecture 2, a Millennium Prize Problem 3. Here we provide examples of new fundamental results in pure mathematics that have been discovered with the assistance of machine learning—demonstrating a method by which machine learning can aid mathematicians in discovering new conjectures and theorems. We propose a process of using machine learning to discover potential patterns and relations between mathematical objects, understanding them with attribution techniques and using these observations to guide intuition and propose conjectures. We outline this machine-learning-guided framework and demonstrate its successful application to current research questions in distinct areas of pure mathematics, in each case showing how it led to meaningful mathematical contributions on important open problems: a new connection between the algebraic and geometric structure of knots, and a candidate algorithm predicted by the combinatorial invariance conjecture for symmetric groups 4. Our work may serve as a model for collaboration between the fields of mathematics and artificial intelligence (AI) that can achieve surprising results by leveraging the respective strengths of mathematicians and machine learning.

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Research works printed but not linked: 38

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Cited by

Metadata

Authors
Davies, A., Veličković, P., Buesing, L., Blackwell, S., Zheng, D., Tomašev, N., Tanburn, R., Battaglia, P., Blundell, C., Juhász, A., Lackenby, M., Williamson, G., Hassabis, D., & Kohli, P.
Venue
Nature
Publisher
Springer Science and Business Media LLC
Published
2021-12-01
Volume
600
Issue
7887
Pages
70-74
ISSN
  • 0028-0836 (ISSN-L)
  • 1476-4687
DOI
10.1038/s41586-021-04086-x
OpenAlex
W3215285253
Cited by
451
References
3
FWCI
26.02
Type
journal article
Language
en
Open access
hybrid
Licence

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