1. The Riemann Hypothesis is a famous unsolved problem in mathematics concerning the zeros of the Riemann zeta function $\zeta(s)$.\n\n2. The hypothesis states that all non-trivial zeros of $\zeta(s)$ have their real part equal to $\frac{1}{2}$. In other words, if $\zeta(s) = 0$ and $s$ is a non-trivial zero, then $s = \frac{1}{2} + it$ for some real number $t$.\n\n3. The Riemann zeta function is defined for complex numbers $s = \sigma + it$ with $\sigma > 1$ by the infinite series $$\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}$$ and can be analytically continued to other values of $s$ except $s=1$.\n\n4. The importance of the hypothesis lies in its deep connection to the distribution of prime numbers, as the zeros of $\zeta(s)$ influence the error term in the prime number theorem.\n\n5. Despite extensive numerical evidence supporting the hypothesis and its central role in number theory, it remains unproven to this day.