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We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years.
K. Bull, Y. H. He, V. Jejjala and C. Mishra, “Machine Learning CICY Threefolds,” Phys. Lett. B
1903
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Y. H. He and S. J. Lee, “Distinguishing elliptic fibrations with AI,” Phys. Lett. B
1904
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1905
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1905
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1905
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1906
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A. Ashmore, Y. H. He and B. A. Ovrut, “Machine learning Calabi-Yau metrics,” Fortsch. Phys
1910
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A. Whitehead, B. Russell,
1910
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1911
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1912
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G. Lample, F. Charton “Deep Learning for Symbolic Mathematics”, arXiv:1912.01412 [cs.SC]
1912
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K. Gödel, “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I.” Monatshefte für Mathematik und Physik 38: 173-198 (1931)
1931
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A. Church, “An Unsolvable Problem of Elementary Number Theory”. Amer. J. of Math. 58 (2): 345 - 363 (1936)
1936
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A. M. Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem”, Proc. LMS, 2, 42, pp. 230-65 (1937)
1937
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A. Newell, J. Shaw, H. Simon, Computer programme (1956) & “Report on a general problem-solving program,” Proc. Int. Conf. Information Processing, pp. 256 - 264 (1959)
1959
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B. Birch, P. Swinnerton-Dyer, “Notes on Elliptic Curves (II)”, J. Reine Angew. Math. 165 (218): 79 - 108 (1965); experiments on EDSAC-2, Cambridge
1965
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P. Martin-Löf, “An intuitionistic theory of types: predicative part, Logic Colloquium” (Bristol, 1973), 73–118. Studies in Logic and the Foundations of Maths, Vol. 80, Amsterdam, 1975
1975
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K. Appel, W. Haken, “Every Planar Map is Four Colorable. I. Discharging”, Illin. J. of Maths, 21 (3): 429 – 490; K. Appel, W. Haken, J. Koch, “Every Planar Map is Four Colorable. II. Reducibilit”, pp491–567, (1977)
1977
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T. Coquand, “An analysis of Girard’s paradox,” Proc. IEEE Symposium on Logic in Computer Science, 227 - 236 (1986)
1986
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P. Candelas, A. M. Dale, C. A. Lutken, R. Schimmrigk, “Complete Intersection Calabi-Yau Manifolds,” Nucl. Phys. B
1994
Earlier work this paper cites.
V. Batyrev, L. Borisov, “Mirror duality and string theoretic Hodge numbers”. Inv. Math. 126 (1): 183-203 (1996)
1996
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M. Newborn,
2001
Earlier work this paper cites.
M. Agrawal, N. Kayal, N. Saxena, “PRIMES is in P”, Annals of Mathematics. 160 (2): 781 - 793, 2002
2002
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M. Kreuzer and H. Skarke, “Complete classification of reflexive polyhedra in four-dimensions,” Adv. Theor. Math. Phys
2002
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S. Shelah, “Classification theory and the number of nonisomorphic models”, Studies in Logic and the Found. of Maths, vol. 92, IX, 1.19, p.49 (1990)
2003
Cited alongside, same era.
2003
Cited alongside, same era.
2003
Cited alongside, same era.
M. Larfors and R. Schneider, “Explore and Exploit with Heterotic Line Bundle Models,” Fortsch. Phys
2003
Cited alongside, same era.
2012
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V. Jejjala, A. Kar and O. Parrikar, “Deep Learning the Hyperbolic Volume of a Knot,” Phys. Lett. B
2012
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2012
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2012
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2003
Cited alongside, same era.
2004
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G. Leibniz,
2004
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2005
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2006
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2006
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2006
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2006
Cited alongside, same era.
2012
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G. Gonthier et al., “Formal Proof—The Four- Color Theorem” Not. AMS, 2005
2013
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Ian Goodfellow, Yoshua Bengio, Aaron Courville,
2016
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2017
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Y. H. He, “Deep-Learning the Landscape,” arXiv:1706.02714 [hep-th]
2017
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D. Krefl and R. K. Seong, “Machine Learning of Calabi-Yau Volumes,” Phys. Rev. D
2017
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F. Ruehle, “Evolving neural networks with genetic algorithms to study the String Landscape,” JHEP
2017
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2018
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The GAP Group,
2018
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2019
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2019
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2019
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C. N. Yang, M. L. Ge and Y. H. He, Ed. “Topology and Physics,” with contributions from Atiyah, Penrose, Witten, et al., WS 2019. ISBN: 978-981-3278-49-3
2019
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q.v., some of the author’s talks at StringData 2020
2020
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R. Iten, T. Metger, H. Wilming, L. del Rio, R. Renner, “Discovering Physical Concepts with Neural Networks”, Phys. Rev. Lett. 124, 010508, 2020
2020
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F. Ruehle, “Data science applications to string theory,” Phys. Rept
2020
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F. Barbaresco, F. Nielsen, Ed,
2021
Closest in time.
Y.-H. He, Manag. Ed.,
2021
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A. Tanaka, A. Tomiya, K. Hashimoto,
2021
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