Axiom
Foundations and logic
A statement assumed without proof, taken as a starting point from which other results are derived.
What is usually left out
Axioms are chosen, not discovered, and changing them changes what is provable. Euclidean and hyperbolic geometry differ by a single axiom about parallel lines, and both are internally consistent, so neither choice is the correct one — they simply describe different objects. "Self-evident" is a historical description of what people hoped axioms would be, not a requirement of one; the axiom of choice is accepted despite consequences almost nobody finds obvious.