Advertisement

Mathematics and the Triumph of the Human Intellect

  • Clifford Cunningham
Chapter

Abstract

A mathematician being inspired to solve a problem. Frontispiece of Algebra by Abel Burja (1786)

Keyword

Mathematics and the Triumph of the Human Intellect 

References

  1. Aspray, W., & Kitcher, P. (Eds.). (1988). History of philosophy of modern mathematics. In Minnesota Studies in the Philosophy of Science (Vol. XI). Minneapolis: University of Minnesota Press.Google Scholar
  2. Becker, C. (1932). The heavenly city of the eighteenth century philosophers. New Haven: Yale University Press.Google Scholar
  3. Bell, E. T. (1937). Men of mathematics. New York: Simon & Schuster.zbMATHGoogle Scholar
  4. Bolyai, F. (1851). Kurzer Grundriss eines Versuchs. No publisher given, M. Vaserhely, Romania.Google Scholar
  5. Buehler, W. K. (1981). Gauss: A biographical study. New York: Springer.CrossRefGoogle Scholar
  6. Bujarski, G. T. (1972). Polish liberalism, 1815–1823. The Polish Review, 17(2), 3–37.Google Scholar
  7. Burja, A. (1786). Der selbstlernende Algebrist. Berlin: Lagarde and Friedrich.Google Scholar
  8. Cajori, F. (1897). A history of elementary mathematics with hints on methods of teaching. New York: Macmillan.zbMATHGoogle Scholar
  9. Craig, H. (1936). The enchanted glass: The Elizabethan mind in literature. New York: Oxford University Press.Google Scholar
  10. D’Alembert, J. (1751). Preliminary discourse. In Encyclopedie, ou Dictionnaire raisonne des sciences, des arts et metiers (Vol. 1). Paris: Briasson.Google Scholar
  11. D’Alembert, J. (1766). Mélanges de Litterature, d’Histoire et de Philosophie. Amsterdam: Zacharie Chatelain & Sons.Google Scholar
  12. Danielson, D. (2011). Ramus, Rheticus, and the Copernican connection. In S. J. Reid & E. A. Wilson (Eds.), Ramus, pedagogy and the liberal arts: Ramism in Britain and the wider world (pp. 153–170). Farnham: Ashgate.Google Scholar
  13. Daston, L. (1988). Classical probability in the enlightenment. Princeton: Princeton University Press.Google Scholar
  14. Débarbat, S., & Dumont, S. (2014). Johann Karl Burckhardt, un Allemand de Gotha a Paris. Almagest, 5(2), 8–25.CrossRefGoogle Scholar
  15. Devlin, K. (2002). Kurt Gödel—Separating truth from proof in mathematics. Science, 298, 1899–1900.CrossRefGoogle Scholar
  16. Diderot, D. (1754). Pensees sur l’Interpretation de la Nature [English edition: 1999, Thoughts on the interpretation of nature, D. J. Adams, trans.). Manchester: Clinamen Press.Google Scholar
  17. Dubyago, A. (1961). The determination of orbits. New York: Macmillan.Google Scholar
  18. Dunnington, G. W. (1937). Carl Friedrich Gauss, inaugural lecture on astronomy. Baton Rouge: Louisiana State University Press.Google Scholar
  19. Euler, L. (1744). Theoria motuum planetarum et cometarum. Berlin: Ambrosius Haude.Google Scholar
  20. Gell-Mann, M. (2002). Some adventures among the elementary particles. Presidential Lecture, Florida International University, Miami. Delivered January 23, 2002.Google Scholar
  21. Godwin, W. (1831). Thoughts on man, his nature, productions, and discoveries. London: Effingham Wilson.Google Scholar
  22. Goedel, K. (1961). Collected works (Vol. III (1981)). Oxford: Oxford University Press.Google Scholar
  23. Goethe, W. (1994). From my life: Poetry and truth (R. R. Heitner, Trans.). Princeton: Princeton University Press.Google Scholar
  24. Golland, L., & Golland, R. (1993). Euler’s troublesome series: An early example of the use of trigonometric series. Historia Mathematica, 20, 54–67.MathSciNetCrossRefzbMATHGoogle Scholar
  25. Grattan-Guinness, I. (1983). Euler’s mathematics in French science 1795–1815. In J. J. Burckhardt, E. A. Fellmann, & W. Habicht (Eds.), Leonhard Euler 1707–1783 (pp. 395–409). Basel: Birkhauser Verlag.Google Scholar
  26. Grattan-Guinness, I. (2002). Landmark writings in western mathematics 1640–1940. Amsterdam: Elsevier.zbMATHGoogle Scholar
  27. Gregory, F. (2006). Origins and nature of fries’ philosophy of science. In M. Friedman & A. Nordmann (Eds.), The Kantian legacy in nineteenth-century science (pp. 81–100). Cambridge: Massachusetts Institute of Technology.Google Scholar
  28. Hahn, R. (1998). A scientist responds to his skeptical crisis: Laplace’s philosophy of science. In J. van der Zande & R. Popkin (Eds.), The skeptical tradition around 1800 (pp. 187–201). Boston: Kluwer.CrossRefGoogle Scholar
  29. Harvey, G. (1577). Ciceronianus. London: Henrici Binneman.Google Scholar
  30. Hooykaas, R. (1999). Fact, faith and fiction in the development of science. Dordrecht: Springer.CrossRefGoogle Scholar
  31. Johnson, F. R. (1937). Astronomical thought in renaissance England. Johns Hopkins Press. Reprinted 1968 by Octagon Books, New York.Google Scholar
  32. Kepler, J. (1627). Rudolphine tables. Ulm: Jonae Saurii.Google Scholar
  33. Kramer, E. (1982). The nature and growth of modern mathematics. Princeton: Princeton University Press.zbMATHGoogle Scholar
  34. Laplace, P.-S. (1798–1827). Traite de Mecanique Celeste, five volumes. Paris: Chez J.B.M. Duprat.Google Scholar
  35. Loemker, L. (1972). Struggle for synthesis: The seventeenth century background of Leibniz’s synthesis of order and freedom. Cambridge: Harvard University Press.CrossRefGoogle Scholar
  36. Mandelbrot, B. (2012). The Fractalist: Memoir of a Scientific Maverick. NY: Pantheon.zbMATHGoogle Scholar
  37. Manley, L. (1980). Convention 1500–1750. Cambridge: Harvard University Press.CrossRefGoogle Scholar
  38. Marsden, B. (1995). Eighteenth- and nineteenth-century developments in the theory and practice of orbit determination. In General history of astronomy, Part B (Vol. 2, pp. 181–190). Cambridge: Cambridge University Press.Google Scholar
  39. Newton, I. (1704). Opticks. London: Sam. Smith & Benj. Walford, Royal Society.zbMATHGoogle Scholar
  40. Olbers, W. (1797). Abhandlung über die leichteste und bequemste Methode die Bahn eines Cometen aus einigen Beobachtungen zu berechnen (Computation of the paths of comets). Weimar: Verlage des Industrie-Comptoirs. Published in English in: The Quarterly Journal of Science. This appeared in installments between 1820 and 1823.Google Scholar
  41. Ong, W. (1958). Ramus: Method, and the decay of dialogue. Cambridge: Harvard University Press.Google Scholar
  42. Ong, W. (1962). The barbarian within. New York: Macmillan.Google Scholar
  43. Patrick, G. T. W. (1889). The fragments of the work of Heraclitus of Ephesus on Nature. Baltimore: N. Murray.CrossRefGoogle Scholar
  44. Pulte, H. (2006). Kant, fries, and the expanding universe of science. In M. Friedman & A. Nordmann (Eds.), The Kantian legacy in nineteenth-century science (pp. 101–122). Cambridge: Massachusetts Institute of Technology.Google Scholar
  45. Quillet, C. (1655). Calvidii Leti Callipsedia. Leyden. Callipaedia: A poem. Written in Latin, made English by N. Rowe, Esq., 1712. London: E. Sanger and E. Curil.Google Scholar
  46. Ramus, P. (1569). Scholarum mathematicarum, libri unus et triginta. Basel: Episcopius.Google Scholar
  47. Saur, G. (1705). Difficultates physicae cartesianae, thesibus inauguralibus philosophicis propositae (Difficulties of Cartesian physics subjected to peripatetic inquiry). Würzburg: Kleyer.Google Scholar
  48. Stenger, V. (2013). Atheism and the physical sciences. In S. Bullivant & M. Ruse (Eds.), The Oxford handbook of atheism (pp. 432–448). Oxford: Oxford University Press.Google Scholar
  49. Wells, G. (1978). Goethe and the development of science, 1750–1900. Science in History (Vol. 5). Alphen an den Rijn: Sijthoff & Noordhoff.Google Scholar
  50. Wigner, E. (1960). The unreasonable effectiveness of mathematics in the natural sciences. Communications in Pure and Applied Mathematics, 13, 1–14.ADSCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Clifford Cunningham
    • 1
  1. 1.Ft. LauderdaleUSA

Personalised recommendations