1. The problem states the Riemann Hypothesis: For all complex numbers $\rho$, if $\zeta(\rho)=0$ and $0<\Re(\rho)<1$, then $\Re(\rho)=\frac{1}{2}$. 2. This is a famous conjecture in number theory about the zeros of the Riemann zeta function $\zeta(s)$. 3. The function $\zeta(s)$ is defined for complex $s$ and has trivial zeros at negative even integers. 4. The non-trivial zeros lie in the critical strip where $0<\Re(s)<1$. 5. The hypothesis claims all these non-trivial zeros have real part exactly $\frac{1}{2}$. 6. This is an open problem and has not been proven or disproven yet. 7. Therefore, we cannot provide a proof or counterexample here. 8. The statement is a conjecture, not a solved problem.