Is God a Mathematician? (39 page)

Livio, M. 2002.
The Golden Ratio: The Story of Phi, the World’s Most Astonishing Number
(New York: Broadway Books).

———. 2005.
The Equation That Couldn’t Be Solved
(New York: Simon & Schuster).

Lottin, J. 1912.
Quetelet: Staticien et Sociologue
(Louvain: Institut Supérieur de Philosophie).

MacHale, D. 1985.
George Boole: His Life and Work
(Dublin: Boole Press Limited).

Machamer, P. 1998. In Machamer, P., ed.
The Cambridge Companion to Galileo
(Cambridge: Cambridge University Press).

Manning, H. P. 1914.
Geometry of Four Dimensions
(London: Macmillan). Reprinted 1956 (New York: Dover Publications).

Maor, E. 1994.
e: The Story of a Number
(Princeton: Princeton University Press).

McMullin, E. 1998. In Machamer, P., ed.
The Cambridge Companion to Galileo
(Cambridge: Cambridge University Press).

Mekler, S., ed. 1902.
Academicorum Philosophorum Index Herculanensis
(Berlin: Weidmann).

Menasco, W., and Rudolph, L. 1995.
American Scientist
, 83 (January–February), 38.

Mendel, G. 1865. “Experiments in Plant Hybridization,” http://www.mendelweb.org/Mendel.plain.html.

Merton, R. K. 1993.
On the Shoulders of Giants: A Shandean Postscript
(Chicago: University of Chicago Press).

Messer, R., and Straffin, P. 2006.
Topology Now
(Washington, D.C.: Mathematical Association of America).

Miller, V. R., and Miller, R. P., eds. 1983.
Descartes, Principles of Philosophy
(Dordrecht: Reidel).

Mitchell, J. C. 1990. In van Leeuwen, J.,
Handbook of Theoretical Computer Science
(Cambridge, Mass.: MIT Press).

Monk, R. 1990.
Ludwig Wittgenstein: The Duty of Genius
(London: Jonathan Cape).

Moore, G. H. 1982.
Zermelo’s Axiom of Choice: Its Origins, Development, and Influence
(New York: Springer-Verlag).

Morgenstern, O. 1971. Draft “Memorandum from Mathematica.” Subject: History of the naturalization of Kurt Gödel. Institute for Advanced Study, Princeton, NJ.

Morris, T. 1999.
Philosophy for Dummies
(Foster City, Calif.: IDG Books).

Motte, A. 1729.
Sir Isaac Newton’s Mathematical Principles of Natural Philosophy and His System of the World.
Revised by F. Cajori, 1947 (Berkeley: University of California Press). Also appeared as Newton, I. 1995.
The Principia
(New York: Prometheus Books).

Mueller, I. 1991. In Bowen, A., ed.
Science and Philosophy in Classical Greece
(London: Garland).

———. 1992. In Kraut, R., ed.
The Cambridge Companion to Plato
(Cambridge: Cambridge University Press).

———. 2005. In Koestier, T., and Bergmans, L., eds.
Mathematics and the Divine: A Historical Study
(Amsterdam: Elsevier).

Nagel, E., and Newman, J. 1959.
Gödel’s Proof
(New York: Routledge & Kegan Paul). Republished 2001 (New York: New York University Press).

Netz, R. 2005. In Koetsier, T., and Bergmans, L., eds.
Mathematics and the Divine: A Historical Study
(Amsterdam: Elsevier).

Netz, R., and Noel, W. 2007.
The Archimedes Codex: How a Medieval Prayer Book Is Revealing the True Genius of Antiquity’s Greatest Scientist
(Philadelphia: Da Capo Press).

Neuwirth, L. 1979.
Scientific American
, 240 (June), 110.

Newman, J. R. 1956.
The World of Mathematics
(New York: Simon & Schuster).

Newton, Sir I. 1729.
Mathematical Principles of Natural Philosophy.
Translated by I. B. Cohen and A. Whitman, 1999 (Berkeley: University of California Press).

———. 1730.
Opticks, or A Treatise of the Reflections, Refractions, Inflec
tions and Colours of Light
, 4th ed. (London: G. Bell). Republished 1952 (New York: Dover Publications).

Nicolson, M. 1935.
Modern Philology
, 32(3), 233.

Obler, L. K., and Gjerlow, K. 1999.
Language and the Brain
(Cambridge: Cambridge University Press).

O’Connor, J. J., and Robertson, E. F. 2003. “Peter Guthrie Tait.” http://www-history.mcs.st-andrews.ac.uk/Biographies/Tait.html.

———. 2005. “Hermann Günter Grassmann.” http://www-history.mcs.st-andrews.ac.uk/Biographies/Grassmann.html.

———. 2007. “G. H. Hardy Addresses the British Association in 1922, part 1.” http://www-history.mcs.st-andrews.ac.uk/Extras/BA_1922_1.html.

Odom, B., Hanneke, D., D’Urso, B., and Gabrielse, G. 2006.
Physical Review Letters
, 97, 030801.

Ooguri, H., and Vafa, C. 2000.
Nuclear Physics B
, 577, 419.

Orel, V. 1996.
Gregor Mendel: The First Geneticist
(New York: Oxford University Press).

Overbye, D. 2000.
Einstein in Love: A Scientific Romance
(New York: Viking).

Pais, A. 1982.
Subtle Is the Lord: The Science and Life of Albert Einstein
(Oxford: Oxford University Press).

Panek, R. 1998.
Seeing and Believing: How the Telescope Opened Our Eyes and Minds to the Heavens
(New York: Viking).

Paulos, J. A. 2008.
Irreligion: A Mathematician Explains Why the Arguments for God Just Don’t Add Up
(New York: Hill and Wang).

Penrose, R. 1989.
The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics
(Oxford: Oxford University Press).

———. 2004.
The Road to Reality: A Complete Guide to the Laws of the Universe
(London: Jonathan Cape).

Perko, K. A., Jr. 1974.
Proceedings of the American Mathematical Society
, 45, 262.

Pesic, P. 2007.
Beyond Geometry: Classic Papers from Riemann to Einstein
(Mineola, N.Y.: Dover Publications).

Peterson, I. 1988.
The Mathematical Tourist: Snapshots of Modern Mathematics
(New York: W. H. Freeman and Company).

Petsche, J.-J. 2006.
Grassmann
(Basel: Birkhäuser Verlag).

Pinker, S. 1994.
The Language Instinct
(New York: William Morrow and Company).

Plato. Ca. 360 BC.
The Republic.
Translated by A. Bloom, 1968 (New York: Basic Books).

Plutarch. Ca. 75 AD. “Marcellus.” Translated by J. Dryden. In Clough, A. H., ed. 1992.
Plutarch’s Lives
(New York: Modern Library).

Poincaré, H. 1891.
Revue Générale des Sciences Pures et Appliquées
2, 769. The article is reprinted in English in Pesic, P., 2007.
Beyond Geometry.

Porphyry. Ca. 270 AD.
Life of Pythagoras.
In Hadas, M., and Smith, M., eds. 1965.
Heroes and Gods
(New York: Harper and Row).

Proclus. Ca. 450.
Proclus: A Commentary on the First Book of Euclid’s “Elements.”
Translated by G. Morrow, 1970. (Princeton: Princeton University Press).

Przytycki, J. H. 1992. Aportaciones Matemáticas Comunicaciones, 11, 173.

Putnam, H. 1975.
Mathematics, Matter and Method: Philosophical Papers
, vol. 1 (Cambridge: Cambridge University Press), 60.

Quetelet, L. A. J. 1828.
Instructions Populaires sur le Calcul des Probabilités
(Brussels: H. Tarbier & M. Hayez).

Quine, W. V. O. 1966.
The Ways of Paradox and Other Essays
(New York: Random House).

———. 1982.
Methods of Logic
, 4th ed. (Cambridge, Mass.: Harvard University Press).

Radelet-de Grave, P., ed. 2005. “Bernoulli-Edition.” http://www.ub.unibas.ch/spez/bernoull.htm.

Ramachandran, V. S., and Blakeslee, S. 1999.
Phantoms of the Brain
(New York: Quill).

Randall, L. 2005.
Warped Passages: Unraveling the Mysteries of the Universe’s Hidden Dimensions
(New York: Ecco).

Raskin, J. 1998. “Effectiveness of Mathematics.” http://jef.raskincenter.org/unpublished/effectiveness_mathematics.html.

Raymond, E. S. 2005. “The Utility of Mathematics.” http://www.catb.org/~esr/writings/utility-of-math.

Redondi, P. 1998. In Machamer, P.
The Cambridge Companion to Galileo
(Cambridge: Cambridge University Press).

Rees, M. J. 1997.
Before the Beginning
(Reading, Mass.: Addison-Wesley).

Reeves, E. 2008.
Galileo’s Glassworks: The Telescope and the Mirror
(Cambridge, Mass.: Harvard University Press).

Renon, L., and Felliozat, J. 1947.
L’Inde Classique: Manuel des Études Indiennes
(Paris: Payot).

Rescher, N. 2001.
Paradoxes: Their Roots, Range, and Resolution
(Chicago: Open Court).

Resnik, M. D. 1980.
Frege and the Philosophy of Mathematics
(Ithaca: Cornell University Press).

Reston, J. 1994.
Galileo: A Life
(New York: HarperCollins).

Ribenboim, P. 1994.
Catalan’s Conjecture
(Boston: Academic Press).

Ricoeur, P. 1996.
Synthese
, 106, 57.

Riedweg, C. 2005.
Pythagoras: His Life and Influence.
Translated by S. Rendall (Ithaca: Cornell University Press).

Rivest, R., Shamir, A., and Adleman, L. 1978.
Communications of the Association for Computing Machinery
, 21(2), 120.

Rodis-Lewis, G. 1998.
Descartes: His Life and Thought
(Ithaca: Cornell University Press).

Ronan, M. 2006.
Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics
(New York: Oxford University Press).

Rosenthal, J. S. 2006.
Struck by Lightning: The Curious World of Probabilities
(Washington, D.C.: Joseph Henry Press).

Ross, W. D. 1951.
Plato’s Theory of Ideas
(Oxford: Clarendon Press).

Rouse Ball, W. W. 1908.
A Short Account of the History of Mathematics
, 4th ed. Republished 1960 (Mineola, N.Y.: Dover Publications).

Rucker, R. 1995.
Infinity and the Mind: The Science and Philosophy of the Infinite
(Princeton: Princeton University Press).

Russell, B. 1912.
The Problems of Philosophy
(London: Home University Library). Reprinted 1997 by Oxford University Press (Oxford).

———. 1919.
Introduction to Mathematical Philosophy
(London: George Allen and Unwin). Reprinted 1993, edited by J. Slater (London: Routledge). Reprinted 2005 (New York: Barnes & Noble).

———. 1945.
History of Western Philosophy.
Reprinted 2007 (New York: Touchstone).

Sainsbury, R. M. 1988.
Paradoxes
(Cambridge: Cambridge University Press).

Sarrukai, S. 2005.
Current Science
, 88(3), 415.

Schmitt, C. B. 1969. “Experience and Experiment: A Comparison of Zabarella’s Views with Galileo’s in
De Motu.
”
Studies in the Renaissance
, 16, 80.

Sedgwick, W. T., and Tyler, H. W. 1917.
A Short History of Science
(New York: The Macmillan Company).

Shapiro, S. 2000.
Thinking about Mathematics: The Philosophy of Mathematics
(Oxford: Oxford University Press).

Shea, W. R. 1972.
Galileo’s Intellectual Revolution: Middle Period, 1610–1632
(New York: Science History Publications).

———. 1998. In Machamer, P., ed.
The Cambridge Companion to Galileo
(Cambridge: Cambridge University Press).

Sieg, W. 1988. “Hilbert’s Program Sixty Years Later.”
Journal of Symbolic Logic,
53, 349.

Smolin, L. 2001.
Three Roads to Quantum Gravity
(New York: Basic Books).

———. 2006.
The Trouble with Physics: The Rise of String Theory, The Fall of Science, and What Comes Next
(Boston: Houghton Mifflin).

Sobel, D. 1999.
Galileo’s Daughter
(New York: Walker & Company).

Sommerville, D. M. Y. 1929.
An Introduction to the Geometry of N Dimensions
(London: Methuen).

Sorell, T. 2005.
Descartes Reinvented
(Cambridge: Cambridge University Press).

Sorensen, R. 2003.
A Brief History of the Paradox: Philosophy and the Labyrinths of the Mind
(Oxford: Oxford University Press).

Sossinsky, A. 2002.
Knots: Mathematics with a Twist
(Cambridge, Mass.: Harvard University Press).

Stanley, T. 1687.
The History of Philosophy
, ninth section. Published in 1970 as a photographic facsimile under the title
Pythagoras: His Life and Teachings
(Los Angeles: The Philosophical Research Society).

Steiner, M. 2005. In Shapiro, S., ed.
The Oxford Handbook of Philosophy of Mathematics and Logic
(Oxford: Oxford University Press).

Stewart, I. 2004.
Galois Theory
(Boca Raton, Fla.: Chapman & Hall/CRC).

———. 2007.
Why Beauty Is Truth: A History of Symmetry
(New York: Perseus Books).

Stewart, J. A. 1905.
The Myths of Plato
(London: Macmillan and Co.).

Stigler, S. M. 1997. In
Académie Royale de Belgique, Bulletin de la Classe des Sciences, Mémoires
, collection 8(3), 47.

Strohmeier, J., and Westbrook, P. 1999.
Divine Harmony
(Berkeley, Calif.: Berkeley Hills Books).

Stukeley, W. 1752.
Memoirs of Sir Isaac Newton’s Life.
Reprinted 1936 (London: Taylor and Francis).

Summers, D. W. 1995.
Notices of the American Mathematical Society
, 42(5), 528.

Swerdlow, N. 1998. In Machamer, P., ed.
The Cambridge Companion to Galileo
(Cambridge: Cambridge University Press).

Tabak, J. 2004.
Probability and Statistics: The Science of Uncertainty
(New York: Facts on File).