Mirror Symmetry and Other Miracles in Superstring Theory


The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam’s ‘no miracles argument’ that, I argue, many string theorists in fact espouse in some form or other. String theory has generated many surprising, useful, and well-confirmed mathematical ‘predictions’—here I focus on mirror symmetry and the mirror theorem. These predictions were made on the basis of general physical principles entering into string theory. The success of the mathematical predictions are then seen as evidence for the framework that generated them. I shall attempt to defend this argument, but there are nonetheless some serious objections to be faced. These objections can only be evaded at a considerably high (philosophical) price.

This is a preview of subscription content, access via your institution.


  1. 1.

    Achinstein, P.: Explanation v. prediction: which carries more weight? in: PSA: Proceeding of the Biennial Meeting of the Philosophy of Science Association, vol. 1994. Volume Two: Symposia and Invited Papers, pp. 156–164 (1994)

  2. 2.

    Atiyah, M.F.: The Geometry and Physics of Knots. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  3. 3.

    Baker, A.: Are there genuine mathematical explanations of physical phenomena? Mind 114, 223–237 (2005)

    MathSciNet  Article  Google Scholar 

  4. 4.

    Ballman, W.: Lectures on Kähler Manifolds. ESI Lectures in Mathematics and Physics. American Mathematical Society, Providence (2006)

    Google Scholar 

  5. 5.

    Bangu, S.I.: Inference to the best explanation and mathematical realism. Synthese 160, 13–20 (2008)

    MATH  Article  Google Scholar 

  6. 6.

    Brush, S.: Prediction and theory evaluation: the case of light bending. Science 246, 1124–1129 (1989)

    ADS  Article  Google Scholar 

  7. 7.

    Brush, S.: Dynamics of theory change: the role of predictions. in: PSA: Proceeding of the Biennial Meeting of the Philosophy of Science Association, vol. 1994. Volume Two: Symposia and Invited Papers, pp. 133–145 (1994)

  8. 8.

    Brush, S.: Why was relativity accepted? Phys. Perspective 1, 184–214 (1999)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  9. 9.

    Candelas, P., Horowitz, G., Strominger, A., Witten, E.: Vacuum configurations for superstrings. Nucl. Phys. B 258, 46–74 (1985)

    MathSciNet  ADS  Article  Google Scholar 

  10. 10.

    Cartwright, N., Frigg, R.: String theory under scrutiny. Phys. World 20, 14–15 (2007)

    Google Scholar 

  11. 11.

    Colyvan, M.: Mathematical recreation versus mathematical knowledge. In: Leng, M., Paseau, A., Potter, M. (eds.) Mathematical Knowledge, pp. 109–122. Oxford University Press, Oxford (2007)

    Google Scholar 

  12. 12.

    Cox, D.A., Katz, S.: Mirror Symmetry and Algebraic Geometry. American Mathematical Society, Providence (1999)

    Google Scholar 

  13. 13.

    Darwin, C.: The Origin of Species (1859). Collier Press (1962)

  14. 14.

    Dawid, R.: Scientific realism in the age of string theory. Phys. Philos. 11, 1–35 (2007)

    Google Scholar 

  15. 15.

    Dirac, P.A.M.: The evolution of the physicist’s picture of nature. Sci. Am. 208(5), 45–53 (1963)

    ADS  Article  Google Scholar 

  16. 16.

    Engler, G.: Quantum field theories and aesthetic disparity. Int. Stud. Philos. Sci. 15(1), 51–63 (2001)

    MathSciNet  MATH  Article  Google Scholar 

  17. 17.

    Feynman, R.P.: QED. The Strange Theory of Light and Matter. Princeton University Press, Princeton (1988)

    Google Scholar 

  18. 18.

    Field, H.: Science Without Numbers. Basil Blackwell, Oxford (1980)

    Google Scholar 

  19. 19.

    Galison, P.: Mirror symmetry: persons, values, and objects. In: Norton Wise, M., et al. (eds.) Growing Explanations: Historical Perspectives on Recent Science, pp. 23–61. Duke University Press, Durham (1999)

    Google Scholar 

  20. 20.

    Green, M., Schwarz, J., Witten, E.: Superstring Theory: Volume 1, Introduction. Cambridge University Press, Cambridge (1988)

    Google Scholar 

  21. 21.

    Greene, B.: Aspects of Quantum Geometry. In: Phong, D.H., Vinet, L., Yau, S.-T. (eds.) Mirror Symmetry III, pp. 1–67. American Mathematical Society, Providence (1999)

    Google Scholar 

  22. 22.

    Hand, E.: String Theory Hints at Explanation for Superconductivity. Nature 25(11), 114008-21 (2009)

    Google Scholar 

  23. 23.

    Hedrich, R.: The internal and external problems of string theory. J. Gen. Philos. Sci. 38, 261–278 (2007)

    MathSciNet  Article  Google Scholar 

  24. 24.

    Hori, K., Katz, S., Klemm, A., Vafa, C., Vakil, R., Zaslow, E.: Mirror Symmetry. American Mathematical Society, Providence (2003)

    Google Scholar 

  25. 25.

    Katz, S.: Enumerative Geometry and String Theory. Student Mathematical Library, vol. 32. American Mathematical Society, Providence (2006)

    Google Scholar 

  26. 26.

    Lian, B.H., Liu, K., Yau, S.-T.: The Candelas-de la Ossa-Green-Parkes formula. Nucl. Phys. B: Proc. Suppl. 67(1–3), 106–114 (2000)

    MathSciNet  ADS  Google Scholar 

  27. 27.

    Lipton, P.: Testing hypotheses: prediction and prejudice. Science 307, 21–22 (2005)

    Article  Google Scholar 

  28. 28.

    Maddy, P.: Naturalism in Mathematics. Oxford University Press, Oxford (1997)

    Google Scholar 

  29. 29.

    Manin, Y.: Reflections on arithmetical physics. In: Dita, P., Georgescu, V. (eds.) Conformal Invariance and String Theory, pp. 293–303. Academic Press, New York (1989)

    Google Scholar 

  30. 30.

    Manin, Y.: Interrelations between mathematics and physics. Soc. Math. Fr. 3, 157–168 (1998)

    MathSciNet  Google Scholar 

  31. 31.

    McCallister, J.W.: Dirac and the aesthetic evaluation of theories. Methodol. Sci. 23(2), 87–102 (1990)

    Google Scholar 

  32. 32.

    Morrow, J., Kodaira, K.: Complex Manifolds. American Mathematical Society, Providence (1971)

    Google Scholar 

  33. 33.

    Musgrave, A.: Logical versus historical theories of confirmation. Br. J. Philos. Sci. 25, 1–23 (1974)

    Article  Google Scholar 

  34. 34.

    Myers, R.C., Vázquez, S.E.: Quark soup Al Dente: applied superstring theory. Class. Quantum Gravity 25(11), 114008-21 (2008)

    ADS  Article  Google Scholar 

  35. 35.

    Olive, D.I., West, P.C.: Duality and Supersymmetric Theories. Publications of the Newton Institute, No. 18. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  36. 36.

    Polchinski, J.: String Theory, vol. 2. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  37. 37.

    Polyakov, A.M.: Quantum geometry of bosonic strings. Phys. Lett. B 103(3), 207–210 (1981)

    MathSciNet  ADS  Google Scholar 

  38. 38.

    Polyakov, A.M.: Quantum geometry of fermionic strings. Phys. Lett. B 103(3), 211–213 (1981)

    MathSciNet  ADS  Google Scholar 

  39. 39.

    Putnam, H.: What is Mathematical Truth? Reprinted in Mathematics, Matter, and Method, pp. 60–78. Cambridge University Press, Cambridge (1979)

    Google Scholar 

  40. 40.

    Quine, W.V.O.: The philosophical bearing of modern logic. In: Klibansky, R. (ed.) Philosophy in the Mid-Century, vol. 1. Nuova Italia, Florence (1958)

    Google Scholar 

  41. 41.

    Rickles, D., Schindler, S.: Physics as good as sex? Reconsidering the scientific status of string theory (forthcoming)

  42. 42.

    Riordan, M.: Stringing physics along. Phys. World 2007, 38–39 (2007)

    Google Scholar 

  43. 43.

    Schellekens, A.N.: The emperor’s last clothes? Overlooking the string theory landscape. Rep. Prog. Phys. 71, 1–13 (2008)

    MathSciNet  Article  Google Scholar 

  44. 44.

    Schrödinger, E.: The philosophy of experiment. Il Nuovo Cimento 1(1), 5–15 (1955)

    Article  Google Scholar 

  45. 45.

    Schwarz, J.: Superstrings—an overview. In: Second Aspen Winter Particle Physics Conference, pp. 269–276. The New York Academy of Sciences, New York (1987)

    Google Scholar 

  46. 46.

    Schwarz, J., Scherk, J.: Dual models for non-hadrons. Nucl. Phys. B 81(1), 118–144 (1974)

    ADS  Article  Google Scholar 

  47. 47.

    Smart, J.J.C.: Between Science and Philosophy. Random House, New York (1968)

    Google Scholar 

  48. 48.

    Smolin, L.: The Trouble with Physics. Houghton Mifflin Company (2006)

  49. 49.

    Sober, E.: Mathematics and indispensability. Philos. Rev. 102(1), 35–57 (1993)

    MathSciNet  Article  Google Scholar 

  50. 50.

    Thomson, W.H.: On vortex motion. Trans. R. Soc. Edin. 25, 217–260 (1869)

    Google Scholar 

  51. 51.

    van Fraassen, B.: The Scientific Image. Oxford University Press, Oxford (1980)

    Google Scholar 

  52. 52.

    Veneziano, G.: String theory: physics or metaphysics? Humana Mente 13, 13–21 (2010)

    Google Scholar 

  53. 53.

    Veneziano, G.: Physics and mathematics: a happily evolving marriage (2010)

  54. 54.

    Whewell, W.: The Philosophy of the Inductive Sciences, vol. 2 (1847), Johnson Reprint Corporation (1967)

  55. 55.

    Yau, S.-T.: Compact three dimensional Kähler manifolds with zero Ricci curvature. In: Bardeen, W.A., White, A. (eds.) Proceedings of the Symposium on Anomalies, Geometry and Topology: Argonne, pp. 395–406. World Scientific, Singapore (1985)

    Google Scholar 

  56. 56.

    Yoneya, T.: Connection of dual models to electrodynamics and gravidynamics. Prog. Theor. Phys. 51(6), 1907–1920 (1973)

    MathSciNet  ADS  Article  Google Scholar 

  57. 57.

    Yoneya, T.: Quantum gravity and the zero-slope limit of the generalized Virasoro model. Lett. Al Nuovo Cimento 8(16), 951–955 (1973)

    Article  Google Scholar 

  58. 58.

    Zahar, E.: Why did Einstein’s programme supercede Lorentz’s? Br. J. Philos. Sci. 24, 95–123 (1973)

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Dean Rickles.

Additional information

For submission to a Foundations of Physics special issue on “Forty Years Of String Theory: Reflecting On the Foundations” (edited by G. ‘t Hooft, E. Verlinde, D. Dieks and S. de Haro).

I would like to thank audiences at the FQXi meeting in the Azores in 2009, and in Toronto, Oxford, Leeds, Utrecht, Bradford, and Sydney for useful discussions. Special thanks to Oswaldo Zapata for his many helpful comments and suggestions. I would also like to acknowledge the Australian Research Council for financial support via discovery grant DP0984930.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Rickles, D. Mirror Symmetry and Other Miracles in Superstring Theory. Found Phys 43, 54–80 (2013). https://doi.org/10.1007/s10701-010-9504-5

Download citation


  • String theory
  • Mirror symmetry
  • No miracles argument