"Mechanics is the reality, mathematics is its description, and physics is the story we tell about it."
Math isn't reality because it is descriptive. Just because you can balance an equation does not mean the hypothesis is valid or representative of reality.
Math describes infinity.
"Does infinity really exist?"
...solve that one real quick 😏
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You need the math to describe something and the physics to explain it. In that sense, mathematical models alone are not enough.
Infinity sounds good. But...
...we have a halting problem.
