How Math Explains the World.pdf

(Marcin) #1

  1. Even the Securities and Exchange Commission warns against them. See http://
    www .sec .gov/ answers/ ponzi .htm.

  2. Carl B. Boyer, A History of Mathematics (New York: John Wiley & Sons, 1991),
    p. 570.

  3. Ibid.

  4. Ibid.

  5. See http:// archives .cnn .com/ 2002/ WORLD/ europe/ 04/ 24/ uk .kissinger/.

  6. L. Wapner, The Pea and the Sun (A Mathematical Paradox) (Wellesley, Mass:
    A. K. Peters, 2005). This is a really thorough and readable exposition of all as-
    pects of the Banach-Tarski theorem—including an understandable treatment of
    the proof—but you’ll still have to be willing to put in the work. Even if you’re not,
    there’s still a lot to like.

  7. See http:// mathworld .wolfram .com/ Zermelo -FraenkelAxioms .html. You’ll have
    to fight your way through standard set theory notation (which is explained at the
    top of the page) in order to understand them, but the axioms themselves are
    pretty basic. There is a link and a further explanation for each axiom. Most
    mathematicians never really worry about these axioms, as the set theory they
    use seems pretty obvious, and are only concerned with finding a useful version
    of the axiom of choice (there are others besides the well-ordering principle). The
    two industry standard versions that I have found most useful are Zorn’s Lemma
    and transfinite induction, and I believe that’s true for the majority of mathema-
    ticians.

  8. H. Weyl, The Continuum (New York: Dover, 1994), p. xii. Hermann Weyl was one
    of the great intellects of the early portion of the twentieth century. He received
    his doctorate from Göttingen; his thesis adviser was David Hilbert. Weyl was an
    early proponent of Einstein’s theory of relativity, and studied the application of
    group theory to quantum mechanics.

  9. Quoted in N. Rose, Mathematical Maxims and Minims, Raleigh N.C.,: Rome
    Press, 1988).


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