"Discoveries" about the mathematical structure of these theories are actually incredibly important even if no current day experiment can conceivably test them. Special and general relativity were discoveries made in this way (at least to an extent), and now general relativity is important for the proper functioning of technology as "trivial and boring" as GPS. Even earlier in our history, much of thermodynamics was developed in a similar fashion.
See the sibling comment for another version of this argument, but finding the weird mathematical coincidences between the competing mathematical theories of nature is very useful. In other words, there are mathematical and logical tests that can be as important as experimental tests for the progress of our understanding of nature.
See the sibling comment for another version of this argument, but finding the weird mathematical coincidences between the competing mathematical theories of nature is very useful. In other words, there are mathematical and logical tests that can be as important as experimental tests for the progress of our understanding of nature.