The Effectiveness of Mathematics in Physics of the Unknown

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Grinbaum, Alexei
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If physics is a science that unveils the fundamental laws of nature, then the appearance of mathematical formulae 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 by employing fundamental principles as constraints within a general mathematical framework. Such studies of the unknown, or blackbox models, demonstrate the unsurprising effectiveness of mathematics on the example of Einstein's principle theories, the S-matrix approach in quantum field theory, effective field theories, and device-independent approaches in quantum information.