prove what poets, philosophers, and psychologists have only been able
to conjecture.
NOTES
1. S e e h t t p : / / w w w - h i s t o r y. m c s. s t - a n d r e w s. a c. u k / B i o g r a p h i e s / G o l d b a c h. h t m l. I
couldn’t resist and looked up Goldbach’s biography. He knew a lot of the greats
and actually did some useful mathematics, but never in the article did I see the
word dilettante, which, it seemed to me, best described him.- Although I couldn’t locate a copy of the book, I recall the story being in I.
 Chernev and F. Reinfeld The Fireside Book of Chess (New York: Simon & Schus-
 ter, 1966).
- See http:// www .wesjones .com/ eoh .htm.
- See http:// www .facstaff .bucknell .edu/ gschnedr/ marxweb .htm.
- I. Asimov Foundation (New York: Gnome Press, 1951); Foundation and Empire
 (New York: Gnome Press, 1952); Second Foundation (New York: Gnome Press,
 1953). Also see http:// www .asimovonline .com/ asimov _home _page .html. This is
 the home page for a complete introduction to Isaac Asimov. One could spend the
 better part of a lifetime reading his books and short stories, and it would proba-
 bly be the better part of the reader’s lifetime.
- See http:// en .wikipedia .org/ wiki/ Catastrophe _theory.This provided an intro-
 duction to catastrophe theory, along with a description of various types of catas-
 trophes. Regrettably, there are no predictions of future catastrophes.
- G. Birkhoff and S. Mac Lane, Algebra (New York: Macmillan, 1979). This is a
 later edition of the book that I used.
248 How Math Explains the World
