I was learning the proofs of the transcendence of $e$ and $\pi$, and I was wondering what would be the usefulness of these results.
So my questions are:
Are there any (relatively simple) application of the transcendence of $e$?
More generally, why is it useful to know that a number $x$ is transcendent?
When I talk about transcendence here, I am putting myself in the simplest case: a real number $x$ being transcendent over $\mathbb Q$.