Riemann Zeta

partial sums spiralling toward the non-trivial zeros on the critical line

Plate II
s0.5 + 14.13i
ζ(s)
|ζ(s)|
Near zero

Each term n−s is a vector; their running sum spirals inward to ζ(s). On the critical line the path closes on the origin exactly at a zero. After 3Blue1Brown · Riemann (1859)