# Definition:Theorem/Mathematics

## Definition

The term **theorem** is used throughout the whole of mathematics to mean a statement which has been proved to be true from whichever axioms relevant to that particular branch.

Note that statements which are taken as axioms in one branch of mathematics may be theorems in others.

It is possible (and this is the ultimate aim of $\mathsf{Pr} \infty \mathsf{fWiki}$) to justify basing the whole of mathematics on a handful of axioms.

## Also see

## Sources

- 1982: P.M. Cohn:
*Algebra Volume 1*(2nd ed.) ... (previous) ... (next): $\S 1.1$: The need for logic