Advancing mathematics by guiding human intuition with AI

Alex Davies (), Petar Veličković, Lars Buesing, Sam Blackwell, Daniel Zheng, Nenad Tomašev, Richard Tanburn, Peter Battaglia, Charles Blundell, András Juhász, Marc Lackenby, Geordie Williamson, Demis Hassabis and Pushmeet Kohli ()
Additional contact information
Alex Davies: DeepMind
Petar Veličković: DeepMind
Lars Buesing: DeepMind
Sam Blackwell: DeepMind
Daniel Zheng: DeepMind
Nenad Tomašev: DeepMind
Richard Tanburn: DeepMind
Peter Battaglia: DeepMind
Charles Blundell: DeepMind
András Juhász: University of Oxford
Marc Lackenby: University of Oxford
Geordie Williamson: University of Sydney
Demis Hassabis: DeepMind
Pushmeet Kohli: DeepMind

Nature, 2021, vol. 600, issue 7887, 70-74

Abstract: 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 conjectures1, most famously in the Birch and Swinnerton-Dyer conjecture2, a Millennium Prize Problem3. 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 groups4. 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.

Date: 2021
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Citations: View citations in EconPapers (14)

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DOI: 10.1038/s41586-021-04086-x

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