The effectiveness of mathematics in physics of the unknown

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 1960.1 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.