Mathematics is Hard to Understand

The words Mathematics is interesting ... and sometimes difficult. began the file Math. That file continued in the vein of Mathematics which refined practical discoveries by drawing attention to beauty. "A Nobel-prize winning physicist put it this way:"

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature. If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in. -Richard Feynman (1918-1988)

However it isn't at all certain that beauty nor precisely communicating truths so that humans can better understand nature are central aspects of mathematics. Through their recent book Lakoff and Nunez communicate deep contradictions in the fundamental structure of the field, drawing upon cognitive science and linguistic reasoning.

  • Lakoff, George and Nunez, Rafael Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being. Basic Books, 2000.

  • A comprehensive overview is found in:

  • Courant, Richard, Robbins, Herbert, Stewart, Ian, What is mathematics?

    Aversion to learning mathematics is the subject of Tobias' work. From her web page "Sheila Tobias first wrote Overcoming Math Anxiety in 1978. ... her updated version, published by W. W. Norton in 1994 (and in paperback in 1995)"; that book and They're not Dumb, They're Different: Stalking the Second Tier communicate many things relevant to the issue of this page. So did Stevenson and Stigler, first through a Scientific American article, then through the book:

    Stevenson, Harold W. and Stigler, James, W., The Learning Gap - Why Our Schools Are Failing and What We Can Learn from Japanese and Chinese Education.

    The following lists several books that supplement those above and convey something of the variety or views about mathematics:

    Beckmann, Petr, A History of Pi, Boulder, Colorado: Golem Press, 1982.

    Dantzig, Tobias, Number The Language of Science, New York, The Macmillan Company, 1930, 1954.

    Davis, Philip J., The Thread, A Mathematical Yarn, Second Edition, NY: Harcourt Brace Javanovich, Publishers, 1983, 1989.

    Adams, James L., Conceptual Blockbusting, San Francisco: W. H. Freeman, 1974.

    Sobel, Dava, Longitude -The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time, London, U.K.: Fourth Estate, 1995.

    Joseph, George Gheverghese, The Crest of the Peacock - Non-European Roots of Mathematics, London UK: I.B. Tauris & Co. Ltd Publishers, 1991.

    Ascher, Marcia, Ethnomathematics, A Multicultural View of Mathematical Ideas, Pacific Grove, CA: Brooks/Cole Publishing Company, Wadsworth, Inc., Belmont, CA, 1991, ISBN 0-534-14880-8.

    Ascher, Marcia, Mathematics Elsewhere, Princeton NJ: Princeton University Press, 2002.

    3/30/09 Version
    ©2009 Allen Klinger