Skip to main content
Log in

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

  • Viewpoint
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Bibliography

  • Bacharach, M. 1883.Abriss zur Geschichte der Potentialtheorie, Würzburg: Thein.

    Google Scholar 

  • Beller, M. 1983. ‘Matrix theory before Schrödinger’,Isis 74, 469–491.

    Article  MATH  MathSciNet  Google Scholar 

  • Colyvan, M. 2001. ‘The miracle of applied mathematics’,Synthese 127, 265–277.

    Article  MATH  MathSciNet  Google Scholar 

  • Chabert, J. L. et al. 1999.A history of algorithms. From the pebble to the microchip, Berlin: Springer.

    Book  MATH  Google Scholar 

  • Corry, L. 1996.Modern algebra and the rise of mathematical structures, Basel: Birkhauser.

    MATH  Google Scholar 

  • 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.].

    Article  MathSciNet  Google Scholar 

  • Dilworth, C. 1994.Scientific progress, Dordrecht: Kluwer.

    Book  Google Scholar 

  • Dyson, F. 1972. ‘Missed opportunities’,Bulletin of the American Mathematical Society 78, 635–652.

    Article  MATH  MathSciNet  Google Scholar 

  • Enriques, F. 1906.The problems of science, Chicago and London: Open Court.

    Google Scholar 

  • French, S. 2000. ‘The reasonable effectiveness of mathematics: partial structures and the application of group theory to physics’,Synthese 125, 103–120.

    Article  MATH  MathSciNet  Google Scholar 

  • Fresnel, A. J. 1866.Oeuvres completes, vol. 1, Paris: Imprimerie Impériale.

    Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • Grattan-Guinness, I. 2004. ‘The mathematics of the past. Distinguishing its history from our heritage’,Historia mathematica, 31, 161–185.

    Article  MathSciNet  Google Scholar 

  • Grattan-Guinness, I. 2007. ‘Equilibrium in mechanics and then in economics, 1860–1920: a good source for analogies?’, in Mosini [2007], 17–44.

  • Grattan-Guinness, I. 2008a. ‘Differential equations and linearity in the 19th and early 20th centuries’,Archives internationales d’histoire des sciences, to appear.

  • 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 

  • 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.

    MATH  Google Scholar 

  • Hamming, R. 1980. ‘The unreasonable effectiveness of mathematics’,The American mathematical monthly, 87, 81–90.

    Article  MathSciNet  Google Scholar 

  • Hawkins, T. W. 1975. ‘Cauchy and the spectral theory of matrices’,Historia mathematica, 2, 1–29.

    Article  MATH  MathSciNet  Google Scholar 

  • Henshaw, J. M. 2006.Does measurement measure up?How numbers reveal and conceal the truth, Baltimore: Johns Hopkins University Press.

    Google Scholar 

  • Hermann, A. 1971.The genesis of quantum theory, Cambridge, Mass.: The MIT Press.

    Google Scholar 

  • Hintikka, J. 2007.Socratic epistemology, Cambridge; Cambridge University Press.

    Book  Google Scholar 

  • 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 

  • Kaushal, R. S. 2003.Structural analogies in understanding nature, New Delhi: Anamaya.

    Google Scholar 

  • Kiesow, H. 1960. Review of Wigner [1960],Zentralblatt für Mathematik 102, 7.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Lesk, A. 2000. ‘The unreasonable effectiveness of mathematics in mo-lecular biology’,The Mathematical Intelligencer 22, no. 2, 28–36.

    Article  MATH  MathSciNet  Google Scholar 

  • Lesk, A. 2001. ‘Compared with what?’,The Mathematical Intelligencer, 23, no. 1, 4.

    Article  Google Scholar 

  • 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.]

    MATH  MathSciNet  Google Scholar 

  • 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 

  • Mackey, G. W. 1992.The scope and history of commutative and noncommutative harmonic analysis, American Mathematical Society and London Mathematical Society.

  • Mathematics 1986. ‘Mathematics: the unifying thread in science’,Notices of the American Mathematical Society 33, 716–733.

    MathSciNet  Google Scholar 

  • Matte Blanco, L. 1975.The unconscious as infinite sets: an essay in bi-logic, London: Duckworth.

    Google Scholar 

  • Medawar, P. B. 1967.The art of the soluble, Harmondsworth: Pelican.

    Google Scholar 

  • Mosini, V. (ed.). 2007.Equilibrium in economics: scope and limits, London: Routledge.

    Google Scholar 

  • 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.

  • Pólya, G. 1954a, 1954b.Mathematics and plausible reasoning, 2 vols., 1st ed., Princeton: Princeton University Press. [2nd ed. 1968.]

    Google Scholar 

  • Pólya, G. 1963.Mathematical methods in science, Washington: MAA.

    Google Scholar 

  • Popper, K. R. 1959.The logic of scientific discovery, London: Hutchinson.

    MATH  Google Scholar 

  • Popper, K. R. 1972.Objective knowledge, Oxford: Clarendon Press.

    Google Scholar 

  • Roche, J. J. 1998.The mathematics of measurement. A critical history, London: Athlone Press.

    MATH  Google Scholar 

  • Ruelle, D. 1988. ‘Is our mathematics natural? The case of equilibrium statistical mechanics’,Bulletin of the American Mathematical Society 19, 259–267.

    Article  MATH  MathSciNet  Google Scholar 

  • Sarukkai, S. 2005. ‘Revisiting the “unreasonable effectiveness” of mathematics’,Current science, 88, 415–422.

    MathSciNet  Google Scholar 

  • 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 

  • Smith, B. (ed.). 1982.Parts and moments. Studies in logic and formal ontology, Munich: Philosophia.

    MATH  Google Scholar 

  • Smithies, F. 1997.Cauchy and the creation of complex function theory, Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Steiner, M. 1998.The applicability of mathematics as a philosophical problem, Cambridge, Mass.: The MIT Press.

    MATH  Google Scholar 

  • Tanner, R. C. H. 1961. ‘Mathematics begins with inequality’,Mathematical Gazette 44, 292–294.

    Article  Google Scholar 

  • Thompson, S. P. 1910.Calculus made easy, 1st ed., London: Macmillans. [Deservedly numerous later eds.].

    Google Scholar 

  • Toeplitz, O. 1963.The calculus. A genetic approach, Chicago: The University of Chicago Press. [German original 1949.].

    MATH  Google Scholar 

  • Velupillai, K. V. 2005. ‘The unreasonable ineffectiveness of mathematics in economics’,Cambridge Journal of Economics 29, 849–872.

    Article  Google Scholar 

  • West, B. J. 1985.An essay on the importance of being nonlinear, Berlin: Springer.

    Book  MATH  Google Scholar 

  • Weyl, H. 1949.Philosophy of mathematics and natural science, Princeton: Princeton University Press.

    MATH  Google Scholar 

  • Weyl, H. 1952.Symmetry, Princeton: Princeton University Press.

    MATH  Google Scholar 

  • Whittaker, E. T. 1927.Analytical dynamics, 3rd ed., Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • 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.].

    Book  Google Scholar 

  • 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.]

    Article  MATH  Google Scholar 

  • Wigner, E. P. 1967.Symmetries and reflections: scientific essays, Bloomington: Indiana University Press.

    Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Wolf, C. J. E. 1889–1891.Mémoires sur le pendule. . ., 2 pts., Paris: Gauthier-Villars.

    Google Scholar 

  • Wussing H. 1984.The genesis of the abstract group concept, Cambridge, Mass.: The MIT Press.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ivor Grattan-Guinness.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grattan-Guinness, I. Solving wigner’s mystery: The reasonable (though perhaps limited) effectiveness of mathematics in the natural sciences. The Mathematical Intelligencer 30, 7–17 (2008). https://doi.org/10.1007/BF02985373

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02985373

Keywords

Navigation