- was proposed by Bernhard Riemann (1859), and is a conjecture about the distribution of the zeros of the Riemann zeta function.

The Riemann hypothesis asserts that all interesting solutions of the equation :

$$ {\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}},} $$

lie on a certain vertical straight line.

Expressed as : “Every nontrivial zero of the Riemann zeta function has real part 1/2”

Or, the analytic continuation of the provided infinite series is hypothesized to have non-trivial solutions that all have a real part of one half.

It remains unproved whether the hypothesis is true or false.

Full details at Wikipedia

An essay on the hypothesis can be found here courtesy University of Washington