Notes, Credits, and
Bibliographical Sources

Main source on Pythagoras and the Pythagoreans:

The Pythagorean Sourcebook and Library, compiled and translated by Kenneth Sylvan Guthrie, introduced and edited by David R. Fideler. Grand Rapids, MI: Phanes Press, 1987.

Additional sources:

W.K.C. Guthrie, A History of Greek Philosophy, Vol. 1, The Earlier Presocratics and the Pythagoreans. Cambridge: Cambridge University Press, 1962.

Charles H. Kahn, Pythagoras and the Pythagoreans: A Brief History. Indianapolis, IN: Hackett Publishing, 2001.

Chapter 1

Source on the history of the Fifteen Puzzle:

Y. I. Perelman, Fun with Math and Physics. Moscow: Mir Publishers, 1988.

Chapter 2

Illustration (Greek coin): Courtesy of the Philosophical Research Society.

Chapter 4

Proclus’ quote from Ivor Thomas, Greek Mathematical Works, Vol. I, Thales to Euclid. Great Britain: Fletcher & Son, 1939, p. 155.

Giovanni Belzoni’s book was published in London by John Murray.

Chapter 8

Epigraph from George Johnston Allman, Greek Geometry from Thales to Euclid. Dublin: Hodges, Figgis & Co., 1889.

Proof of the incommensurability of the diagonal based on an argument in Lucio Russo, La Rivoluzione Dimenticata. Milan: Feltrinelli, 1996, p. 53.

Chapter 10

Flaws in random number generators based on:

Alan M. Ferrenberg, David. P. Landau, and Y. Joanna Wong, “Monte Carlo Simulations: Hidden Errors from ‘Good’ Random Number Generators,” Physical Review Letters 69, no. 23, December 7, 1992, pp. 3382–3384.

William Bown, “Gambling on the Wrong Numbers from Monte Carlo.” New Scientist 24, April 1993, p. 16.

Chapter 11

Thorp’s groundbreaking result and its consequences based on:

Gregory Chaitin, “A Random Walk in Arithmetic.” New Scientist, March 24, 1990.

C. S. Calude and G. J. Chaitin, “Randomness Everywhere.” Nature 400, July 22, 1999, pp. 319–320.

Marcus Chown, “The Omega Man.” New Scientist, March 10, 2001, pp. 29–31.

For more on randomness in mathematics, see Chaitin’s latest books:

Meta Math!: The Quest for Omega. New York: Pantheon, 2005.

Thinking about Gödel and Turing: Essays on Complexity, 1970–2007. Singapore: World Scientific, 2007.

Chapter 13

Epigraph from K. S. Guthrie, The Pythagorean Sourcebook and Library, 1987, p. 117.

Chapter 14

The excerpts from “Song of the Hindu” on pages 89–90 are from Return of the Aryans, by Bhagwan S. Gidwani, and they are reproduced courtesy of the publishers (Penguin Books India) and the author.

Chapter 16

Excerpts from the book on the beginnings of Greek mathematics are quotations (slightly edited) from Árpád Szabó, The Beginnings of Greek Mathematics. Dordrecht, Holland / Boston, MA: D. Reidel Publishing, 1978, pp. 186–191.

Chapter 17

The figure showing the illustration from the medieval book reproduced from Jerôme Carcopino, De Pythagore aux apôtres : étude sur la conversion du monde romain. Paris: Flammarion, 1956, p. 116, with permission from the publisher.

Chapter 19

Passage from Homer quoted from Homer: The Odyssey, World’s Classics, Walter Shewring, translator. Oxford and New York: Oxford University Press, 1980, p. 101.

Chapter 20

Description of the Neo-Pythagorean basilica based on:

George H. Chase, “Archaeology in 1917.” The Classical Journal 14, no. 4 (January 1919), pp. 250–251.