1. The Riemann Hypothesis is a famous unsolved problem in mathematics. 2. It concerns the zeros of the Riemann zeta function, which is defined for complex numbers $s$ with real part greater than 1 by the infinite series $$\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}.$$ 3. This function can be extended to other values of $s$ (except $s=1$) by analytic continuation. 4. The hypothesis states that all non-trivial zeros of the Riemann zeta function have their real part equal to $\frac{1}{2}$. 5. In other words, if $\zeta(s) = 0$ and $s$ is a non-trivial zero, then $$\text{Re}(s) = \frac{1}{2}.$$ 6. This conjecture has deep implications in number theory, especially in the distribution of prime numbers. 7. Despite extensive numerical evidence supporting it, the Riemann Hypothesis remains unproven. Final answer: The Riemann Hypothesis asserts that all non-trivial zeros of the Riemann zeta function lie on the critical line where the real part of $s$ is $\frac{1}{2}$.