>>10486187The main difference is that I can try to form a very different approach to reality that is equally valid despite having a widely different form. For instance, Classical Mechanics is perfectly valid at the scale we apply it, but so is using Quantum Mechanics directly. Those two approaches have, however, fundamental differences ; an equation I use in physics is valid within certain hypothesis that depends on the scale of the object. F = ma (or Hamilton equations...) is a universal truth about mechanics, but in experience, I might see some slight variations from what I predicted.
However, in the case of maths, the perimeter of a circle is always pi*r2. This relation is true, was true, and will always be true if we accept the axioms we invented to formalise mathematics.
