, Volume 196, Issue 3, pp 973–989 | Cite as

The effectiveness of mathematics in physics of the unknown

  • Alexei GrinbaumEmail author


If physics is a science that unveils the fundamental laws of nature, then the appearance of mathematical concepts in its language can be surprising or even mysterious. This was Eugene Wigner’s argument in 1960. I show that another approach to physical theory accommodates mathematics in a perfectly reasonable way. To explore unknown processes or phenomena, one builds a theory from fundamental principles, employing them as constraints within a general mathematical framework. The rise of such theories of the unknown, which I call blackbox models, drives home the unsurprising effectiveness of mathematics. I illustrate it on the examples of Einstein’s principle theories, the S-matrix approach in quantum field theory, effective field theories, and device-independent approaches in quantum information.


Mathematics Physics Wigner Principle theory S-matrix Effective field theory Device-independence Unknown 



Many thanks to Bryan Roberts for helpful remarks.


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Authors and Affiliations

  1. 1.CEA-Saclay/IRFU/LARSIMGif-sur-YvetteFrance

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