- 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.”
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