Building on work by Fermat and Huygens, Hamiltontransformed the study of geometrical opticsin his very first paper, presented when still inhis teens. His ‘characteristic function’ was ananalytical way to describe wavefronts, and in hishands a powerful tool to look at families of raysrather than isolated ones. His prediction of internaland external conical refraction in somecrystals and its spectacular verification in a fewmonths established his reputation among his contemporaries.This formulation of optics uncoveredmany general properties, not easy to seein the conventional method of tracing individualrays. The deepest outcome of his early opticalwork was a parallel view of the mechanics ofparticles, which played a fundamental role in thebirth of quantum mechanics and continues to bethe standard framework for classical mechanicsup to the present time.