The Mathematical Intelligencer

, Volume 30, Issue 3, pp 7–17

Solving wigner’s mystery: The reasonable (though perhaps limited) effectiveness of mathematics in the natural sciences

Viewpoint

Abstract

The Viewpoint column offers mathematicians the opportunity to write about any issue of interest to the international mathematical community. Disagreement and controversy are welcome. The views and opinions expressed here, however, are exclusively those of the author, and neither the publisher nor the editor-in-chief endorses or accepts responsibility for them. Viewpoint should be submitted to the editor-in-chief, Chandler Davis.

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Bibliography

  1. Bacharach, M. 1883.Abriss zur Geschichte der Potentialtheorie, Würzburg: Thein.Google Scholar
  2. Beller, M. 1983. ‘Matrix theory before Schrödinger’,Isis 74, 469–491.CrossRefMATHMathSciNetGoogle Scholar
  3. Colyvan, M. 2001. ‘The miracle of applied mathematics’,Synthese 127, 265–277.CrossRefMATHMathSciNetGoogle Scholar
  4. Chabert, J. L. et al. 1999.A history of algorithms. From the pebble to the microchip, Berlin: Springer.CrossRefMATHGoogle Scholar
  5. Corry, L. 1996.Modern algebra and the rise of mathematical structures, Basel: Birkhauser.MATHGoogle Scholar
  6. Dantzig, G. B. 1982. ‘Reminiscences about the origins of linear programming’,Operational research letters. I, 43–48. [Slightly rev. ed. in A. Bachem, M. Grotschel, and B. Corte (eds.),Mathematical programming. The state of the art, Berlin: Springer, 1983, 78–86.].CrossRefMathSciNetGoogle Scholar
  7. Dilworth, C. 1994.Scientific progress, Dordrecht: Kluwer.CrossRefGoogle Scholar
  8. Dyson, F. 1972. ‘Missed opportunities’,Bulletin of the American Mathematical Society 78, 635–652.CrossRefMATHMathSciNetGoogle Scholar
  9. Enriques, F. 1906.The problems of science, Chicago and London: Open Court.Google Scholar
  10. French, S. 2000. ‘The reasonable effectiveness of mathematics: partial structures and the application of group theory to physics’,Synthese 125, 103–120.CrossRefMATHMathSciNetGoogle Scholar
  11. Fresnel, A. J. 1866.Oeuvres completes, vol. 1, Paris: Imprimerie Impériale.Google Scholar
  12. Grattan-Guinness, I. 1990.Convolutions in French mathematics, 1800–1840. From the calculus and mechanics to mathematical analysis and mathematical physics, 3 vols., Basel: Birkhäuser; Berlin: Deutscher Verlag der Wissenschaften.Google Scholar
  13. Grattan-Guinness, I. 1992a. ‘Scientific revolutions as convolutions? A sceptical enquiry’, in S. S. Demidov, M. Folkerts, D. E. Rowe, and C. J. Scriba (eds.),Amphora. Festschrift fur Hans Wussing zu seinem 65. Geburtstag, Basel: Birkhäuser, 279–287.Google Scholar
  14. Grattan-Guinness, I. 1992b. ‘Structure-similarity as a cornerstone of the philosophy of mathematics’, in J. Echeverria, A. Ibarra, and T. Mormann (eds.),The space of mathematics. Philosophical, epistemological, and historical explorations, Berlin, New York: de Gruyter, 91–111.Google Scholar
  15. Grattan-Guinness, I. 1994. (ed.),Companion encyclopaedia of the history and philosophy of the mathematical sciences, London: Routledge. [Repr. Baltimore: Johns Hopkins University Press, 2003.].Google Scholar
  16. Grattan-Guinness, I. 2004. ‘The mathematics of the past. Distinguishing its history from our heritage’,Historia mathematica, 31, 161–185.CrossRefMathSciNetGoogle Scholar
  17. Grattan-Guinness, I. 2007. ‘Equilibrium in mechanics and then in economics, 1860–1920: a good source for analogies?’, in Mosini [2007], 17–44.Google Scholar
  18. Grattan-Guinness, I. 2008a. ‘Differential equations and linearity in the 19th and early 20th centuries’,Archives internationales d’histoire des sciences, to appear.Google Scholar
  19. Grattan-Guinness, I. 2008b. ‘On the early work of William Thomson: mathematical physics and methodology in the 1840s’, in R. G. Flood, M. McCartney, A. Whitaker (eds.),Lord Kelvin: life, labours and legacy, Oxford: Oxford University Press, 44–55, 314–316.Google Scholar
  20. Grattan-Guinness, I. with the collaboration of Ravetz, J. R. 1972.Joseph Fourier 1768–1830. A survey of his life and work, based on a critical edition of his monograph on the propagation of heat, presented to the Institut de France in 1807, Cambridge, Mass.: MIT Press.MATHGoogle Scholar
  21. Hamming, R. 1980. ‘The unreasonable effectiveness of mathematics’,The American mathematical monthly, 87, 81–90.CrossRefMathSciNetGoogle Scholar
  22. Hawkins, T. W. 1975. ‘Cauchy and the spectral theory of matrices’,Historia mathematica, 2, 1–29.CrossRefMATHMathSciNetGoogle Scholar
  23. Henshaw, J. M. 2006.Does measurement measure up?How numbers reveal and conceal the truth, Baltimore: Johns Hopkins University Press.Google Scholar
  24. Hermann, A. 1971.The genesis of quantum theory, Cambridge, Mass.: The MIT Press.Google Scholar
  25. Hintikka, J. 2007.Socratic epistemology, Cambridge; Cambridge University Press.CrossRefGoogle Scholar
  26. Holland, J. R. 1975.Adaptation in natural and artificial systems. An introductory analysis with applications to biology, control and artificial intelligence, Ann Arbor: The University of Michigan Press.Google Scholar
  27. Kaushal, R. S. 2003.Structural analogies in understanding nature, New Delhi: Anamaya.Google Scholar
  28. Kiesow, H. 1960. Review of Wigner [1960],Zentralblatt für Mathematik 102, 7.Google Scholar
  29. Knobloch, E. 2000. ‘Analogy and the growth of mathematical knowledge’, in E. Grosholz, H. Breger (eds.),The growth of mathematical knowledge, Dordrecht: Kluwer, 295–314.CrossRefGoogle Scholar
  30. Lesk, A. 2000. ‘The unreasonable effectiveness of mathematics in mo-lecular biology’,The Mathematical Intelligencer 22, no. 2, 28–36.CrossRefMATHMathSciNetGoogle Scholar
  31. Lesk, A. 2001. ‘Compared with what?’,The Mathematical Intelligencer, 23, no. 1, 4.CrossRefGoogle Scholar
  32. Mackey, G. W. 1978. ‘Harmonic analysis as the exploitation of symmetry: A historical survey’,Rice University Studies 64, 73–228. [Repr. in [1992], 1–158.]MATHMathSciNetGoogle Scholar
  33. Mackey, G. W. 1985. ‘Herman Weyl and the application of group theory to quantum mechanics’, in W. Deppert et al. (eds.),Exact sciences and their philosophical foundations, Kiel: Peter Lang, 131–159. [Repr. in [1992], 159–188.]Google Scholar
  34. Mackey, G. W. 1992.The scope and history of commutative and noncommutative harmonic analysis, American Mathematical Society and London Mathematical Society.Google Scholar
  35. Mathematics 1986. ‘Mathematics: the unifying thread in science’,Notices of the American Mathematical Society 33, 716–733.MathSciNetGoogle Scholar
  36. Matte Blanco, L. 1975.The unconscious as infinite sets: an essay in bi-logic, London: Duckworth.Google Scholar
  37. Medawar, P. B. 1967.The art of the soluble, Harmondsworth: Pelican.Google Scholar
  38. Mosini, V. (ed.). 2007.Equilibrium in economics: scope and limits, London: Routledge.Google Scholar
  39. Poisson, S. D. 1823. ‘Sur la distribution de la chaleur dans un anneau homogène et d’une èpaisseur constante... ’,Connaissance des temps (1826), 248–257.Google Scholar
  40. Pólya, G. 1954a, 1954b.Mathematics and plausible reasoning, 2 vols., 1st ed., Princeton: Princeton University Press. [2nd ed. 1968.]Google Scholar
  41. Pólya, G. 1963.Mathematical methods in science, Washington: MAA.Google Scholar
  42. Popper, K. R. 1959.The logic of scientific discovery, London: Hutchinson.MATHGoogle Scholar
  43. Popper, K. R. 1972.Objective knowledge, Oxford: Clarendon Press.Google Scholar
  44. Roche, J. J. 1998.The mathematics of measurement. A critical history, London: Athlone Press.MATHGoogle Scholar
  45. Ruelle, D. 1988. ‘Is our mathematics natural? The case of equilibrium statistical mechanics’,Bulletin of the American Mathematical Society 19, 259–267.CrossRefMATHMathSciNetGoogle Scholar
  46. Sarukkai, S. 2005. ‘Revisiting the “unreasonable effectiveness” of mathematics’,Current science, 88, 415–422.MathSciNetGoogle Scholar
  47. Schwartz, J. 1962. ‘The pernicious influence of mathematics on science’, in E. Nagel et al. (eds.),Logic, methodology and philosophy of science, Stanford: Stanford University Press, 356–360. [Repr. in R. Hersh (ed.),18 unconventional essays on the nature of mathematics, New York: Springer, 2005, 231–235.]Google Scholar
  48. Smith, B. (ed.). 1982.Parts and moments. Studies in logic and formal ontology, Munich: Philosophia.MATHGoogle Scholar
  49. Smithies, F. 1997.Cauchy and the creation of complex function theory, Cambridge: Cambridge University Press.CrossRefMATHGoogle Scholar
  50. Steiner, M. 1998.The applicability of mathematics as a philosophical problem, Cambridge, Mass.: The MIT Press.MATHGoogle Scholar
  51. Tanner, R. C. H. 1961. ‘Mathematics begins with inequality’,Mathematical Gazette 44, 292–294.CrossRefGoogle Scholar
  52. Thompson, S. P. 1910.Calculus made easy, 1st ed., London: Macmillans. [Deservedly numerous later eds.].Google Scholar
  53. Toeplitz, O. 1963.The calculus. A genetic approach, Chicago: The University of Chicago Press. [German original 1949.].MATHGoogle Scholar
  54. Velupillai, K. V. 2005. ‘The unreasonable ineffectiveness of mathematics in economics’,Cambridge Journal of Economics 29, 849–872.CrossRefGoogle Scholar
  55. West, B. J. 1985.An essay on the importance of being nonlinear, Berlin: Springer.CrossRefMATHGoogle Scholar
  56. Weyl, H. 1949.Philosophy of mathematics and natural science, Princeton: Princeton University Press.MATHGoogle Scholar
  57. Weyl, H. 1952.Symmetry, Princeton: Princeton University Press.MATHGoogle Scholar
  58. Whittaker, E. T. 1927.Analytical dynamics, 3rd ed., Cambridge: Cambridge University Press.MATHGoogle Scholar
  59. Wigner, E. P. 1931.Gruppentheorie und ihre Anwendung auf die Quantenmechanik tier Atomspektren, Braunschweig: Vieweg. [Rev. English trans.:Group theory and its application to the quantum mechanics of atomic spectra, New York: Academic Press, 1959.].CrossRefGoogle Scholar
  60. Wigner, E. P. 1960. ‘The unreasonable effectiveness of mathematics in the natural sciences’,Communications on pure and applied mathematics, 13, 1–14. [Repr. in [1967], 222–237; and inPhilosophical reflections and syntheses (ed. G. Emch), Berlin: Springer, 1995, 534–548.]CrossRefMATHGoogle Scholar
  61. Wigner, E. P. 1967.Symmetries and reflections: scientific essays, Bloomington: Indiana University Press.Google Scholar
  62. Wilson, C. A. 1980a, 1980b. ‘Perturbation and solar tables from Lacaille to Delambre: the rapprochement of observation with theory’,Archive for history of exact sciences 22, 53–188, 189–304.CrossRefMathSciNetGoogle Scholar
  63. Wolf, C. J. E. 1889–1891.Mémoires sur le pendule. . ., 2 pts., Paris: Gauthier-Villars.Google Scholar
  64. Wussing H. 1984.The genesis of the abstract group concept, Cambridge, Mass.: The MIT Press.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Middlesex University at EnfieldMiddlesexEngland

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