Importance of the Transcendence of $\pi$ and $e$

Question

Why do people care that $\pi$ and $e$ are transcendental?

Answer 1

One use for knowing whether $\pi $ is transcendental is the very old problem of squaring the circle. For thousands of years we were unable to answer it, it was only in $1882$ that we solved it, as a consequence of the Lindemann-Weierstrass theorem.