One way I’ve seen it put, that resonates with me, is that axioms are invented but theorems are discovered. That is nicely self-evident. The idea that axioms are

One way I’ve seen it put, that resonates with me, is that axioms are invented but theorems are discovered. That is nicely self-evident. The idea that axioms are also discovered is … iffy, but it happens in some cases. E.g., discovering that your theory is unsound and the only way to fix it is by adding the obvious axiom.