Millennium Prize Problem

Prompt

Solve the following Millennium Prize Problem: **The Riemann Hypothesis** Prove or disprove that every non-trivial zero of the Riemann zeta function [ \zeta(s)=\sum_{n=1}^{\infty}\frac{1}{n^s} ] (after analytic continuation) has real part exactly equal to [ \operatorname{Re}(s)=\frac{1}{2}. ] Provide a complete, rigorous mathematical proof or a rigorous counterexample.