**Axioms** (together with definitions) forms the basis of mathematical theorems. Every mathematical theorem is **only **proven inside its axiom system.

All mathematics is a sort of if—then language, only true inside the appropriate axiom system.

And there are different sets of axiom systems: Euclidean plane geometry, the Zermelo-Fraenkel axioms for set theory, Kolmogorov’s axioms for probability theory and so on.

The seemingly “absolute truth” of mathematics is an illusion. Playing with “mathematical certainties” outside their field can end in more and more and more illusory certainties.