<p>The standard wave equation describing symmetrical wave propagation in all directions in three dimensions, was discovered by the French scientist d’Alembert, more than 250 years ago. In the 20^th century it became important to search for ‘one-way’ versions of this equation in three dimensions – i.e., an equation describing wave propagation in one direction for all angles, and forbiting it in the opposite direction – for a variety of applications in computational and topological physics. Here, by borrowing techniques from relativistic quantum field theory – in particular, from the Dirac equation –, and starting from Engquist and Majda’s seminal, approximative one-way wave equations, we report the discovery of the exact one-way wave equation in three dimensions. Surprisingly, we find that this equation necessarily – similarly to the innate emergence of spin in the Dirac equation – has a topological nature, giving rise to strong, spin-orbit coupling and locking, and non-vanishing (integer) Chern numbers.</p>