The problem with physics is that everyone is searching for deep philosophical meaning. Just don't: the Nature doesn't owe you any meaning. It doesn't care at all about a bunch of carbon polymers that for some reason tricked itself into thinking it is the center of the universe.
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Mathematics was crafted by humans to be the thing that marvelously works; would be a shame if it finally didn't.
but the applicability yo nature need not be true, and yet it is
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Mathematics isn't just a fun mind exercise. It has almost always been developed in close connection to reality for the sole purpose of solving real-world problems. It only happened in about XIX century that it started progressing slightly towards abstraction and generalization.
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But isn’t this at tension with your original claim
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