Theorems do not live in isolation: they lean on one another, and theses already proved become hypotheses for new theorems. This whole edifice must, however, rest on something that is not proved.
Definition — Theory
A theory is a set of interconnected theorems, whose theses become hypotheses of other theorems, building an architecture of proofs that rests on primitive hypotheses called postulates (or axioms). Postulates are not proved: they are accepted “on mathematical faith”.
At the base, therefore, lie the postulates; from them the first theorems are deduced, which in turn allow others to be proved, in a layered structure.
The postulates (at the bottom) support the theorems, which in turn support others: the theory grows in layers.
Links
Topics: Euclidean geometry
Concepts: Postulate · Theorem · Theory
Skills: Proving