Advertisement

Math Currents in the Brain

  • Misha GromovEmail author
Chapter
Part of the Mathematics, Culture, and the Arts book series (MACUAR)

Abstract

What is mathematics, and how did it originate? Where does the stream of mathematical ideas flow from? What is the ultimate source of mathematics in the brain? These are reminiscent of the ancient question, “What does the Earth rest on?” with our instincts pushing us toward On-a-Giant-Turtle answers.

References

  1. 1.
    Byers, William. How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics. Princeton, NJ: Princeton University Press, 2010.CrossRefzbMATHGoogle Scholar
  2. 2.
    Coombs, Clyde Hamilton, Robyn M. Dawes, and Amos Tversky. Mathematical Psychology: An Elementary Introduction. Englewood Cliffs, NJ: Prentice-Hall: 1970.Google Scholar
  3. 3.
    Dehaene, Stanislas. The Number Sense: How the Mind Creates Mathematics. Oxford: Oxford University Press, 2011.zbMATHGoogle Scholar
  4. 4.
    Devlin, Keith. The Math Instinct: Why You’re a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs). New York: Basic Books, 2006.Google Scholar
  5. 5.
    Gromov, Mikhail. “Mendelian Dynamics and Sturtevant’s Paradigm.” In Geometric and Probabilistic Structures in Dynamics, edited by Keith Burns, Dmitry Dolgopyat, and Yakov Pesin. Vol. 469. Contemporary Mathematics, American Mathematical Society, 2008.Google Scholar
  6. 6.
    ———. “Structures, Learning, and Ergosystems.” Last modified December 30, 2011. www.ihes.fr/~gromov/PDF/ergobrain.pdf.
  7. 7.
    ———. “In a Search for a Structure, Part 1: On Entropy.” Last modified June 25, 2013. http://www.ihes.fr/~gromov/PDF/structre-serch-entropy-july5-2012.pdf
  8. 8.
    ———. “Ergostructures, Ergologic and the Universal Learning Problem.” Last modified October 8, 2013. http://www.ihes.fr/~gromov/PDF/ergologic3.1.pdf.
  9. 9.
    ———. “Quotations and Ideas.” Last modified April 15, 2016. http://www.ihes.fr/~gromov/PDF/quotations2016.pdf.
  10. 10.
    Gromov, Mikhail, and Giancarlo Lucchini. Introduction aux mystères. Paris: Fondation Cartier pour l’Art Contemporain/Actes Sud, 2012.Google Scholar
  11. 11.
    Hadamard, Jacques. The Mathematician’s Mind: The Psychology of Invention in the Mathematical Field. Princeton, NJ: Princeton University Press, 1945.zbMATHGoogle Scholar
  12. 12.
    Haldane, John Burdon Sanderson. The Inequality of Man and Other Essays. London: Chatto & Windus, 1932.Google Scholar
  13. 13.
    Kanerva, Pentti. Sparse Distributed Memory. Boston: MIT Press, 1988.zbMATHGoogle Scholar
  14. 14.
    Koonin, Eugene V. The Logic of Chance: The Nature and Origin of Biological Evolution. Upper Saddle River, NJ: FT Press, 2011.Google Scholar
  15. 15.
    Lakoff, George, and Rafael E. Núñez. Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. New York: Basic Books, 2000.zbMATHGoogle Scholar
  16. 16.
    Luce, R. Duncan. “The mathematics used in mathematical psychology.” The American Mathematical Monthly 71, no. 4 (1964): 364–378.Google Scholar
  17. 17.
    Mărgineanu, Nicolae. Logical and Mathematical Psychology: Dialectical Interpretation of Their Relations. Cluj-Napoca: Editura Presa Universitara Clujeana: 1997.Google Scholar
  18. 18.
    Oudeyer, Pierre-Yves. Aux Sources de la Parole: Auto-Organisation et Évolution. Paris: Odile Jacob, 2013.Google Scholar
  19. 19.
    Oudeyer, Pierre-Yves, Frédéric Kaplan, and Verena V. Hafner. “Intrinsic Motivation Systems for Autonomous Mental Development.” IEEE Transactions on Evolutionary Computation 11, no. 2 (2007): 265–286. Accessed August 1, 2016. http://www.pyoudeyer.com/ims.pdf.
  20. 20.
    Poe, Edgar Allan. “Maelzel’s Chess-Player.” Southern Literary Messenger 2, no. 5 (1836): 318–326.Google Scholar
  21. 21.
    Poincaré, Henri. “Intuition and Logic in Mathematics,” in The Value of Science: Essential Writings of Henri Poincaré. New York: Modern Library, 2001.Google Scholar
  22. 22.
    Ruelle, David. The Mathematician’s Brain. Princeton, NJ: Princeton University Press, 2007.zbMATHGoogle Scholar
  23. 23.
    Schmidhuber, Jürgen. “Formal Theory of Creativity, Fun, and Intrinsic Motivation (1990–2010).” IEEE Transactions on Autonomous Mental Development 2, no. 3 (2010): 230–247. Accessed August 1, 2016. http://www.ece.uvic.ca/~bctill/papers/ememcog/Schmidhuber_2010.pdf.
  24. 24.
    Spalding, Douglas. “On instinct.” Nature 6 (1872): 485–486.CrossRefGoogle Scholar
  25. 25.
    Townsend, James T. “Mathematical psychology: Prospects for the 21st Century: A Guest Editorial.” Journal of Mathematical Psychology 52, no. 5 (2008): 269–280.Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut des Hautes Études ScientifiquesBures-sur-YvetteFrance
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

Personalised recommendations