Universal truths are what mathematics is about. Precise statements which have been established as true are called theorems. And how the truth of a theorem is established is by giving a logically correct proof, deriving the stated conclusion from the stated assumptions, i.e., the hypotheses.
Well, you may ask: what does it mean that a theorem statement is phrased precisely? And what qualifies as a logically correct proof?
You are seeking deeper understanding of mathematics itself. Welcome!