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A human-like artificial intelligence for mathematics

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  • Santiago Alonso-Diaz

    (EGADE Business School, Tecnológico de Monterrey)

Abstract

This paper provides a brief overview of findings in mathematical cognition and how a human-like AI in mathematics may look like. Then, it provides six reasons in favor of a human-like AI for mathematics: (1) human cognition, with all its limits, creates mathematics; (2) human mathematics is insightful, not merely deductive steps; (3) human cognition detects structure in the real world; (4) human cognition can tackle and detect complex problems; (5) human cognition is creative; (6) human cognition considers ethical issues. The paper provides a tentative frame to the question whether human mathematical cognition is relevant for designing an artificial intelligence that works on and creates mathematics.

Suggested Citation

  • Santiago Alonso-Diaz, 2024. "A human-like artificial intelligence for mathematics," Mind & Society: Cognitive Studies in Economics and Social Sciences, Springer;Fondazione Rosselli, vol. 23(1), pages 79-97, December.
    • Handle: RePEc:spr:minsoc:v:23:y:2024:i:1:d:10.1007_s11299-024-00304-x
    DOI: 10.1007/s11299-024-00304-x
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    References listed on IDEAS

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    1. Aldo Rustichini & Katherine E. Conen & Xinying Cai & Camillo Padoa-Schioppa, 2017. "Optimal coding and neuronal adaptation in economic decisions," Nature Communications, Nature, vol. 8(1), pages 1-14, December.
    2. Marco Zorzi & Konstantinos Priftis & Carlo Umiltà, 2002. "Neglect disrupts the mental number line," Nature, Nature, vol. 417(6885), pages 138-139, May.
    3. Samuel J. Cheyette & Steven T. Piantadosi, 2020. "A unified account of numerosity perception," Nature Human Behaviour, Nature, vol. 4(12), pages 1265-1272, December.
    4. Percy K. Mistry & Anthony Strock & Ruizhe Liu & Griffin Young & Vinod Menon, 2023. "Learning-induced reorganization of number neurons and emergence of numerical representations in a biologically inspired neural network," Nature Communications, Nature, vol. 14(1), pages 1-21, December.
    5. Alex Davies & Petar Veličković & Lars Buesing & Sam Blackwell & Daniel Zheng & Nenad Tomašev & Richard Tanburn & Peter Battaglia & Charles Blundell & András Juhász & Marc Lackenby & Geordie Williamson, 2021. "Advancing mathematics by guiding human intuition with AI," Nature, Nature, vol. 600(7887), pages 70-74, December.
    6. Celeste Kidd & Steven T Piantadosi & Richard N Aslin, 2012. "The Goldilocks Effect: Human Infants Allocate Attention to Visual Sequences That Are Neither Too Simple Nor Too Complex," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-8, May.
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