[lowkeynthorough]

Lol that trick also covers much of quantum mechanics, and relativity. (The gauge in “gauge theory” is a basis, btw)

[nimish]

A large amount of mathematics is trying to find the easiest way to express a problem, changing to that view, solving the simpler problem, then going back to your original formulation

Solving indefinite integrals by substitution for example. Justified by the chain rule.