Is God a Mathematician_ - Mario Livio [126]
known for their bitter intrafamily feuds: Described in Hellman 2006.
became known as the problem of the catenary: An excellent description of the problem, and in particular of Huygens’s solution, can be found in Bukowski 2008. The solutions of Bernoulli, Leibniz, and Huygens appear in Truesdell 1960.
“You say that my brother proposed”: Quoted in Truesdell 1960.
in his Philosophical Essay on Probabilities: Laplace 1814 (translated by Truscot and Emory in 1902).
John Graunt (1620–74) was trained: Excellent descriptions of Graunt’s life and work can be found in Hald 1990, Cohen 2006, and Graunt 1662.
Halley’s paper, which had the rather long title: The paper is reprinted in Newman 1956.
Here is how Jakob Bernoulli described: Quoted in Newman 1956. His work is summarized in Todhunter 1865.
Adolphe Quetelet was born: Two excellent books on Quetelet and his work are Hankins 1908 and Lottin 1912. Shorter but also informative pieces can be found in Stigler 1997, Krüger 1987, and Cohen 2006.
“Chance, that mysterious, much abused word”: Quetelet 1828.
was in fact a type that nature: Quetelet wrote in his memoir on the propensity to crime: “If the average man were determined for a nation he would represent the type of that nation; if he could be determined from the ensemble of men, he would represent the type of the entire human race.”
The person who first introduced: For a popular exposition of the work of Galton and Pearson, see Kaplan and Kaplan 2006.
The serious study of probability: Recently published, entertaining popular accounts of probability, its history, and its uses include Aczel 2004, Kaplan and Kaplan 2006, Connor 2006, Burger and Starbird 2005, and Tabak 2004.
in a letter dated July 29, 1654: Todhunter 1865, Hald 1990.
The essence of probability theory: An excellent, popular, brief description of some of the essential principles of probability theory can be found in Kline 1967.
Probability theory provides us with accurate information: The relevance of probability theory to many real-life situations is beautifully described in Rosenthal 2006.
The person who brought probability: For an excellent biography, see Orel 1996.
Mendel published his paper: Mendel 1865. An English translation can be found on the Web page created by R. B. Blumberg at http://www.mendelweb.org.
While some questions related to the accuracy: See Fisher 1936, for example.
the influential British statistician: For a brief description of some of his work see Tabak 2004. Fisher wrote an extremely original, nontechnical article about the design of experiments entitled “Mathematics of a Lady Tasting Tea” (see Fisher 1956).
in his book Ars Conjectandi: For a superb translation see Bernoulli 1713b.
He then proceeded to explain: Reprinted in Newman 1956.
Shaw once wrote an insightful article: The article “The Vice of Gambling and the Virtue of Insurance” appears in Newman 1956.
In a pamphlet entitled The Analyst: The pamphlet was written by George Berkeley in 1734. An edited version by David Wilkins is maintained on the Web; see Berkeley 1734.
Chapter 6. Geometers: Future Shock
In his famous book Future Shock: Toffler 1970.
Hume identified “truths”: Hume 1748.
Kant asked not what we can know: According to Kant, one of the fundamental philosophical tasks is to account for the possibility of synthetic a priori knowledge of mathematical concepts. Among the many references, I note Höffe 1994 and Kuehn 2001 for the general concepts. A good discussion of the application to mathematics can be found in Trudeau 1987.
“Space is not an empirical”: Kant 1781.
The first four Euclidean axioms: For a relatively gentle introduction to Euclidean