The Riemann Hypothesis

The Riemann zeta function $\zeta(s)$ is initially defined for complex numbers $s$ with real part greater than $1$ by the absolutely convergent series $\zeta(s) = \sum_{n=1}^{\infty} n^{-s}$, and admits a unique meromorphic continuation to the entire complex plane with a single simple pole at $s = 1$. The trivial zeros of $\zeta(s)$ are the negative even integers $-2, -4, -6, \ldots$. Prove that every zero $s$ of $\zeta(s)$ that is neither equal to $1$ nor a trivial zero satisfies $\operatorname{Re}(s) = \frac{1}{2}$.