Mathematician here. A standard trick is to look for counterexamples as simple as possible. A usual joke is that if the professor ask a question in a class, the

Mathematician here. A standard trick is to look for counterexamples as simple as possible. A usual joke is that if the professor ask a question in a class, the answer is 0 or 1. (In physics, it's 0 or infinity.) If the very simple counterexample fails, you try to understand why and make a new counterexample that is slightly less simple and solves the problem. And then you iterate until you run out of counterexamples and has proved the theorem.