The lecture traces the development of mathematical physics from the late eighteenth and early nineteenth centuries, emphasizing how mathematical formalisms came to unify diverse physical subjects such as heat conduction, hydrodynamics, elasticity, magnetism, electricity, and light. It focuses on the mathematical dress of physical theories rather than physical hypotheses, following contributions by figures like Euler, Lagrange, Laplace, Poisson, and Fourier, and highlights key analytical tools—differential equations, continuity relations, and potential theory—and the gradual extension of methods across problems while noting later discoveries that prompted new approaches.