ζ(1/2+it) traced as a spiral in the complex plane. Each crossing through the origin is a non-trivial zero. The Riemann Hypothesis: all such zeros lie exactly on the critical line Re(s)=1/2.
t = 0 | zeros found: 0
Riemann 1859: all non-trivial zeros of ζ(s) are conjectured to lie on Re(s)=1/2. First zero: t≈14.135. Computed zeros: 10¹³ verified on critical line (Gourdon 2004). The partial sum ζ_N(s)=Σ n^{-s} (n=1..N) approximates ζ(s) using the Euler-Maclaurin method. The spiral winds around zeros. Connection to prime numbers: ζ(s)=∏(1-p^{-s})^{-1} (Euler product). Zero spacings follow GUE random matrix statistics (Montgomery-Odlyzko law) — a deep link to quantum chaos.