The effectiveness of mathematics in physics of the unknown

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Synthese, ISSN: 0039-7857, Page: 1-17

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Grinbaum, Alexei
Springer Nature
Arts and Humanities; Social Sciences
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article description
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.