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  • Perspective
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AI-driven research in pure mathematics and theoretical physics

Nature Reviews Physics volume 6, pages 546–553 (2024)Cite this article

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Abstract

The past five years have seen a dramatic increase in the usage of artificial intelligence (AI) algorithms in pure mathematics and theoretical sciences. This might appear counter-intuitive as mathematical sciences require rigorous definitions, derivations and proofs, in contrast to the experimental sciences, which rely on the modelling of data with error bars. In this Perspective, we categorize the approaches to mathematical and theoretical discovery as ‘top-down’, ‘bottom-up’ and ‘meta-mathematics’. We review the progress over the past few years, comparing and contrasting both the advances and the shortcomings of each approach. We believe that although the theorist is not in danger of being replaced by AI systems in the near future, the combination of human expertise and AI algorithms will become an integral part of theoretical research.

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Acknowledgements

The author is most grateful to A. Bhattacharya, A. Kosyak and M. Duncan for many valuable comments on the draft. The author thanks many collaborators over the past few years on AI-assisted mathematics, for the great fun and friendship: D. Aggarwal, L. Alessandretti, G. Arias-Tamargo, A. Ashmore, J. Bao, A. Baronchelli, P. Berglund, D. Berman, K. Bull, L. Calmon, H. Chen, S. Chen, A. Constantin, P.-P. Dechant, R. Deen, S. Garoufalidis, E. Heyes, E. Hirst, J. Hofscheier, J. Ipiña, V. Jejjala, A. Kasprzyk, M. Kim, S. Lal, K.-H. Lee, S.-J. Lee, J. Li, A. Lukas, S. Majumder, C. Mishra, G. Musiker, B. Nelson, A. Nestor, T. Oliver, B. Ovrut, T. Peterken, S. Pietromonaco, A. Pozdnyakov, D. Riabchenko, D. Rodriguez-Gomez, H. Sá Earp, M. Sharnoff, T. Silva, E. Sultanow, Y. Xiao, S.-T. Yau and Z. Zaz. The research is funded in part by STFC grant ST/J00037X/2 and the Leverhulme Trust for a project grant.

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  1. London Institute for Mathematical Sciences, Royal Institution, London, UK

    Yang-Hui He  (何楊輝)

  2. Merton College, University of Oxford, Oxford, UK

    Yang-Hui He  (何楊輝)

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  1. Yang-Hui He  (何楊輝)
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Correspondence to Yang-Hui He  (何楊輝).

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He, YH. AI-driven research in pure mathematics and theoretical physics. Nat Rev Phys 6, 546–553 (2024). https://doi.org/10.1038/s42254-024-00740-1

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