Experimental Methods in Proofs

  • Gabriele Lolli


The presence of experimental methods in mathematics has been the leit-motiv of the so called, by Imre Lakatos in [12], renaissance of empiricism in the philosophy of mathematics.


Mathematical Proof Rubber Sheet Notable Property Original Conjecture Parabolic Segment 
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  1. 1.
    B. Cipra: What’s Happening in the Mathematical Sciences, vol. 1 (1993), vol. 2 (1994), vol. 3 (1995-6), vol. 4 (1998-9), (Providence, R.I., AMS 1993-1999)Google Scholar
  2. 2.
    M. Detlefsen and M. Luker: The Four-Color Theorem and Mathematical Proof. The Journal of Philosophy 77 (1980) pp 803–20CrossRefGoogle Scholar
  3. 3.
    E. J. Dijksterhuis: Archimedes (Princeton University Press, Princeton 1987)Google Scholar
  4. 4.
    L. Euler: Specimen de usu observationum in mathesi pura. Novi commentarii academiae scientiarum Petropolitanae, 6 (1756-7), (1761) pp 185–230, with a summary ibidem, pp. 19-21, both in: Opera omnia, ser. I, vol. 2, Commentationes arithmeticae (Teubner, Leipzig 1915) pp. 459-92Google Scholar
  5. 5.
    F. Q. Gouvea: Euler’s Convincing Non-Proofs. Focus, 27, n. 1 (2007) pp. 10–11Google Scholar
  6. 6.
    T. C. Hales: Cannonballs and Honeycombs. Notices AMS 47, 4 (2000) pp 440–9Google Scholar
  7. 7.
    T. Heath: The Works of Archimedes (Dover, New York 1953)Google Scholar
  8. 8.
    T. Heath: A History of Greek Mathematics (1921), vol. 1 (Dover, New York 1981)Google Scholar
  9. 9.
    R. Hersh: Some Proposals for Reviving the Philosophy of Mathematics. Advances in Mathematics 31 (1979) pp. 31–50. Reprinted in [20] pp 9-28CrossRefGoogle Scholar
  10. 10.
    M. Kac and S. M. Ulam: Mathematics and Logic (1968), (Penguin Books, London 1979)Google Scholar
  11. 11.
    I. Lakatos: Proofs and Refutations (Cambridge Univ. Press, Cambridge 1976) Previously published in four parts in The British Journal for the Philosophy of Science 14 (1963-64)Google Scholar
  12. 12.
    I. Lakatos: A Renaissance of Empiricism in the Recent Philosophy of Mathematics. In: Philosophical Papers, 2 voll (Cambridge Univ. Press, Cambridge 1978) Reprinted in [20] pp 29–48Google Scholar
  13. 13.
    G. Pólya: Mathematics and Plausible Reasoning, vol. 1: Induction and Analogy in Mathematics (Princeton Univ. Press, Princeton 1954)Google Scholar
  14. 14.
    H. Putnam: What is Mathematical Truth. In: Philosophical Papers, vol. 1, Mathematics, Matter and Method (Cambridge Univ. Press, Cambridge 1975) Reprinted in [20] pp 49–65Google Scholar
  15. 15.
    E. Rufini: Il “Metodo” di Archimede (Zanichelli, Bologna 1926) Reprinted: (Feltrinelli, Milano 1961)Google Scholar
  16. 16.
    M. Steiner: Mathematical Knowledge (Cornell Univ. Press, Ithaca 1975)Google Scholar
  17. 17.
    E. R. Swart: The Philosophical Implications of the Four-Color Problem. Amer. Math. Monthly 87 (1980) pp 697–707CrossRefGoogle Scholar
  18. 18.
    P. Teller: Computer Proof. The Journal of Philosophy 77 (1980) pp 797–803CrossRefGoogle Scholar
  19. 19.
    T. Tymoczko: The Four-Color Problem and Its Philosophical Significance. The Journal of Philosophy, 76 (1979) pp 57–83CrossRefGoogle Scholar
  20. 20.
    T. Tymoczko (ed): New Directions in the Philosophy of Mathematics (Princeton Univ. Press, Princeton 1998)Google Scholar

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© Springer-Verlag Italia 2008

Authors and Affiliations

  • Gabriele Lolli
    • 1
  1. 1.Universita di TorinoDipartimento di MatematicaTorinoItaly

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