Mathematical physics deals with the “applications of mathematics to problems of physics and the development of mathematical methods suitable for the formulation of physical theories and their applications,” using a mathematical formalism and the tools provided by mathematics itself. So, in other words, natural phenomena are observed, measured, and then analyzed using various mathematical tools.

The history of mathematical physics can be traced back to the origins of the scientific method, when Galileo stated that “the natural world must be described by its own language, and that language is mathematics.” Today, mathematical physics focuses primarily on the development of physics from as general a point of view as possible.

The term “mathematical physics” is often used in a special sense, to define research aimed at solving physics-inspired problems in a mathematically rigorous setting. Mathematical physics in this sense covers a broad spectrum of topics, characterized by the union of pure mathematics with physics. Although related to theoretical physics, mathematical physics emphasizes mathematical rigor as developed in mathematics, while theoretical physics emphasizes connections to experimental physics and observations, often requiring the use of heuristic arguments. Consequently, mathematical physics is the absolute closest branch of physics to mathematics.