Riemann's Hypothesis

Einstein once said “Pure mathematics is, in its way, the poetry of logical ideas.”

I am not a mathematician but I have a deep love for it.

There is a famous open hypothesis in mathematics that's called "Riemann's Hypothesis".

Riemann observed that the frequency of prime numbers is related to the behavior of the function ζ(s) called the Riemann Zeta function. He then suggested that all interesting solutions (excluding the trivial zeros -2,4,...) of the equation ζ(s) = 0 lie on a certain vertical straight line on the complex plane.

You can see this clearly in the picture (where t runs from 0 to 34).

This beautiful connection between the distribution of prime numbers and the roots of an equation in the complex plane is nothing short of amazing.