Is this a good definition for theorem

1. A theorem is a proven mathematical statement.
OR
2. A mathematical statement that is always true.

Which one is better? If these aren't correct definitions, can you please simply explain to me what a theorem is?

Every theorem in mathematics is of the form

if A then B.

Given A and any prior proven theorems(and a set of axioms), it is shown that B follows from A by applying logic and the standard deduction rules.

As to your responses, either one can be used but I prefer #1. It is true, however, that, once a theorem is proven by valid methods, it is "always" true from that point on.

There are no "false" theorems in mathematics.

Hope that helps.

A theorem is supposed to have been proven, so 2 is not a good definition, because there are lots of true statements that have yet to be proved. So, I would say 1 is better.

1 is better

Postulates are mathematical statements that are always true, but they certainly aren't theorems.