> Of course, the reason we invest so much in mathematics is because it is somewhat mysteriously effective for describing the observed world.

Any particular "arbitrary formalized language of symbols" is validated by experiment, either explicitly or implicitly. Humanity/ culture keeps the string games that works and jettison the ones that don't; it is a slow, collaborative process. We have worked out a pretty good "arbitrary formalized language of symbols", but not because we derived these string games or intuited them, but rather because we test them daily.

To be a formalist doesn't imply that a person under-appreciates the mysterious power of mathematics, just that they don't believe in an underlying psuedo-Kantian "truth".

Also, as I understand it, advanced physics is necessarily done formally only, since our intuition is so ridiculous at the atomic scale and all the equations like Schrodingers are only postulated, then verified empirically.

Also, it is snarky and under-informed, but I think of this debate as Hilbert (Hilbert!) and Some Guy.