Is God a Mathematician_ - Mario Livio [129]
“If I am unclear about the nature”: In Waismann 1979.
Kurt Gödel was born: A recent biography is Goldstein 2005. The standard biography has been Dawson 1997.
he published his incompleteness theorems: Excellent books on Gödel’s theorems, their meaning, and their connection with other branches of knowledge include Hofstadter 1979, Nagel and Newman 1959, and Franzén 2005.
“But, despite their remoteness”: Gödel 1947.
Gödel the man was every bit: A comprehensive description of Gödel’s philosophical views and how he related philosophical ideas to the foundations of mathematics can be found in Wang 1996.
“It was in 1946 that Gödel”: Morgenstern 1971.
Now all that existed was an incomplete: This is clearly a huge over-simplification, allowed only in a popular text. In fact, serious attempts in logicism continue even today. These typically assume that many mathematical truths are knowable a priori. See Wright 1997 and Tennant 1997, for example.
Chapter 8. Unreasonable Effectiveness?
Various knots were even given: An interesting book on making knots is Ashley 1944.
The mathematical theory of knots: Vandermonde 1771. An excellent review of the history of knot theory can be found in Przytycki 1992. lively introduction to the theory itself is presented in Adams 1994. popular account is given in Neuwirth 1979, Peterson 1988, and Menasco and Rudolph 1995.
Thomson’s efforts concentrated on formulating: Excellent descriptions are presented by Sossinsky 2002 and Atiyah 1990.
Tait started his classification: Tait 1898, Sossinsky 2002. A brief, well-written biography of Tait can be found in O’Connor and Robertson 2003.
Maxwell offered the following rhyme: Knott 1911.
University of Nebraska professor: Little 1899.
Topology—the rubber-sheet geometry: A technical but still elementary introduction to topology is provided in Messer and Straffin 2006.
the New York lawyer: Perko 1974.
A breakthrough in knot theory came: Alexander 1928.
the prolific English-American mathematician: Conway 1970.
An examination of that relation eventually revealed: Jones 1985.
in a wide range of sciences: For instance, mathematician Louis Kauffman has demonstrated a relationship between the Jones polynomial and statistical physics. An excellent but technical book on physics applications is Kauffman 2001.
The agents that take care: An excellent description of knot theory and the action of enzymes is given in Summers 1995. See also Wasserman and Cozzarelli 1986.
String theory appears to be: For wonderful popular accounts of string theory, its successes and problems, see Greene 1999, Randall 2005, Krauss 2005, and Smolin 2006. For a technical introduction, see Zweibach 2004.
string theorists Hirosi Ooguri and Cumrun Vafa: Ooguri and Vafa 2000.
created an unexpected relation: Witten 1989.
rethought from a purely mathematical perspective: Atiyah 1989; see Atiyah 1990 for a broader perspective.
Eric Adelberger, Daniel Kapner, and their collaborators: Kapner et al. 2007.
Einstein had a very strong reason: There are many excellent expositions of the ideas of special and general relativity. I’ll mention here only a few that I have particularly liked: Davies 2001, Deutsch 1997, Ferris 1997, Gott 2001, Greene 2004, Hawking and Penrose 1996, Kaku 2004, Penrose 2004, Rees 1997, and Smolin 2001. A recent, wonderful description of Einstein the man and his ideas is given in Isaacson 2007. Previous superb depictions of Einstein and his world include Bodanis 2000, Lightman 1993, Overbye 2000, and Pais 1982. or a nice collection of original papers, see Hawking 2007.
The most recent test was the result: Kramer et al. 2006.
a group of physicists at Harvard University: Odom et al. 2006.
In the late 1960s, physicists: An excellent description can be found in Weinberg 1993.
Chapter 9. On the Human Mind, Mathematics, and the Universe
Here is how mathematicians: Davis and Hersh 1981.
representing the Platonic point of view: Hardy 1940.
expressed precisely the opposite perspective: Kasner and Newman 1989.
Those who