The Riemann zeta function ζ(s) = Σ n^{−s} converges for Re(s) > 1, and is extended by analytic continuation to the whole complex plane (minus s=1). Its non-trivial zeros lie in the critical strip 0 < Re(s) < 1. The Riemann Hypothesis (1859) — one of the Millennium Prize Problems — asserts all non-trivial zeros have real part exactly ½. The color map below shows |ζ(s)| in the critical strip; dark rings mark zeros. The vertical line Re(s) = ½ bisects the image.