For over 120 years, the Riemann Hypothesis (RH) has remained unsolved within modern mathematics. This paper argues that the prolonged stalemate is an artifact of a historical ``mathematical game of Telephone.'' Between 1859 and the turn of the 20th century, the foundational understanding of the hypothesis underwent a systemic paradigm shift. It mutated from Riemann's original, structurally locked analytic signal framework into an unconstrained, abstract algebraic sandbox popularized by David Hilbert. By reconstructing the chronological timeline (1859--1900--Present), we demonstrate how modern formalism stripped away the orthogonal Fourier duality and the uncorrupted prime signal that initially dead-bolted the critical coordinate at $a = \frac{1}{2}$, replacing a rigid geometric reality with an oscillating algebraic illusion.