mlsanityData to 7 Oct 2026

A Triumvirate of AI Driven Theoretical Discovery

arXiv 2405.19973 ↗First posted 30 May 2024math.HO cs.AI hep-thcited by 5

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Abstract (arXiv)

Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the 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 discovery as "top-down", "bottom-up" and "meta-mathematics", as inspired by historical examples. We review some of the progress over the last few years, comparing and contrasting both the advances and the short-comings in each approach. We argue that while the theorist is in no way in danger of being replaced by AI in the near future, the hybrid of human expertise and AI algorithms will become an integral part of theoretical discovery.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 61 of its 137 references that are in the map. First posted on arXiv 30 May 2024.

Builds on

61 of 137 references.

References · 61

  1. 2013Efficient Estimation of Word Representations in Vector Spacecited by 4,346
  2. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 536
  3. 2024Large Language Models for Mathematical Reasoning: Progresses and Challengescited by 283
  4. 2019Deep Learning for Symbolic Mathematicscited by 266
  5. 2022End-to-end symbolic regression with transformerscited by 195
  6. 2022A Survey of Deep Learning for Mathematical Reasoningcited by 124
  7. 2024Metacognitive Capabilities of LLMs: An Exploration in Mathematical Problem Solvingcited by 82
  8. 2022Rediscovering orbital mechanics with machine learningcited by 71
  9. 2021Scientific Machine Learning Benchmarkscited by 60
  10. 2020Learning to Unknotcited by 40
  11. 2020Detecting Symmetries with Neural Networkscited by 33
  12. 2023Learning the greatest common divisor: explaining transformer predictionscited by 33
38 more
  1. 2020Neural Network Approximations for Calabi-Yau Metricscited by 32
  2. 2021Machine-Learning Mathematical Structurescited by 25
  3. 2021Nonperturbative renormalization for the neural network-QFT correspondencecited by 24
  4. 2019Machine learning Calabi-Yau metricscited by 23
  5. 2018Machine Learning CICY Threefoldscited by 22
  6. 2020Machine Learning and Computational Mathematicscited by 22
  7. 2017Deep-Learning the Landscapecited by 21
  8. 2020Learning selection strategies in Buchberger's algorithmcited by 20
  9. 2024Machine learning and information theory concepts towards an AI Mathematiciancited by 20
  10. 2018The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learningcited by 19
  11. 2020Quiver Mutations, Seiberg Duality and Machine Learningcited by 19
  12. 2020Machine learning for complete intersection Calabi-Yau manifolds: a methodological studycited by 17
  13. 2019Machine Learning and Big Scientific Datacited by 16
  14. 2019Learning Algebraic Structures: Preliminary Investigationscited by 15
  15. 2021Machine Learning Calabi-Yau Hypersurfacescited by 15
  16. 2020Machine-Learning the Sato--Tate Conjecturecited by 14
  17. 2022Murmurations of elliptic curvescited by 14
  18. 2023Is deep learning a useful tool for the pure mathematician?cited by 14
  19. 2020Machine Learning Lie Structures & Applications to Physicscited by 13
  20. 2020Graph Laplacians, Riemannian Manifolds and their Machine-Learningcited by 12
  21. 2020Disentangling a Deep Learned Volume Formulacited by 12
  22. 2022Fundamental limits to learning closed-form mathematical models from datacited by 12
  23. 2024Rigor with Machine Learning from Field Theory to the Poincar'e Conjecturecited by 12
  24. 2020Explore and Exploit with Heterotic Line Bundle Modelscited by 11
  25. 2020Machine-Learning Dessins d'Enfants: Explorations via Modular and Seiberg-Witten Curvescited by 10
  26. 2021Machine-Learning Non-Conservative Dynamics for New-Physics Detectioncited by 10
  27. 2023AI for Mathematics: A Cognitive Science Perspectivecited by 10
  28. 2023MLFMF: Data Sets for Machine Learning for Mathematical Formalizationcited by 10
  29. 2014Learning to Discover Efficient Mathematical Identitiescited by 9
  30. 2020Machine-Learning Number Fieldscited by 9
  31. 2021Calabi-Yau Metrics, Energy Functionals and Machine-Learningcited by 9
  32. 2022Cluster Algebras: Network Science and Machine Learningcited by 9
  33. 2019Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyercited by 8
  34. 2021Machine Learning Kreuzer--Skarke Calabi--Yau Threefoldscited by 8
  35. 2023Mathematical conjecture generation using machine intelligencecited by 8
  36. 2017(Machine) Learning to Do More with Lesscited by 7
  37. 2020Scientific intuition inspired by machine learning generated hypothesescited by 7
  38. 2021AI Descartes: Combining Data and Theory for Derivable Scientific Discoverycited by 7

50 most cited of 61 All 61 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2025A Multi-Task Evaluation of LLMs' Processing of Academic Text Inputcited by 5
  2. 2026Flow-based Extremal Mathematical Structure Discoverycited by 3
  3. 2025CayleyPy Growth: Efficient growth computations and hundreds of new conjectures on Cayley graphs (Brief version)cited by 1
  4. 2026Deep Reinforcement Learning for Fano Hypersurfacescited by 0
  5. 2026AI and Human Approaches to Mathematical Problem Solvingcited by 0