If mathematics is just a useful tool we made up, then how can it describe the world with perfect accuracy? And how come as soon as you remove mathematics and mathematical equations from physics, physicists can no longer objectively explain or predict anything?
In: Physics
There is a philosophical debate on whether math exist concretely in the world but you answered your own question.
Math is a tool that we can use to model the world. Physics is not this thing that exists as an independent entity, it is the specific form math take when being used to describe physical phenomenon.
Another way to think about it: Physics does not USE math, physics IS math but for the world.
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