# A match not made in heaven: on the applicability of mathematics in physics

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## Abstract

In his seminal 1960 paper, the physicist Eugene Wigner formulated the question of the applicability of mathematics in physics in a way nobody had before. This formulation has been (almost) entirely overlooked due to an exclusive concern with (dis)solving Wigner’s problem and explaining the effectiveness of mathematics in the natural sciences, in one way or another. Many have attempted to attribute Wigner’s unjustified conclusion—that mathematics is unreasonably effective in the natural sciences—to his (dogmatic) formalist views on mathematics. My goal is to show that this reading misses out on Wigner’s highly original formulation of the problem which is presented throughout his body of work in physics as well as in philosophy. This formulation, as I will show, leads us in a new direction in solving the applicability problem.

## Keywords

Applicability of mathematics Wigner’s Puzzle Unreasonable effectiveness Laws of nature Invariance principles## Notes

### Acknowledgments

I thank Tom Donaldson, Krista Lawlor, Solomon Feferman, Michael Friedman, Mark Steiner, José Ferreirós and Jonathan Ettel for their insightful suggestions. My special thanks are to Thomas Ryckman for his enormously useful comments on several revisions of this paper.

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