Yes, the job of a mathematician is not to prove theorems. But rather to find the interesting or beautiful ones.
I'm currently working on my first formal math paper, and I've been spending a lot of time figuring out how to best present the information so that it is comprehendible and easy to read. Things like structure of the paper, wording, notation, and more.
There's probably a lot of time to spend convincing others that your theorem is interesting, too. Some of the most respected works in mathematics after all are thoughtful compilations of previously proven results.