Mathematical physics

The field of study known as mathematical physics focuses on the creation of mathematical techniques that may be applied to challenges in the field of physics. "the application of mathematics to issues in physics and the development of mathematical techniques suited for such applications and for the formulation of physical theories" is how the field is defined by the Journal of Mathematical Physics, which is the leading publication in the area. One alternate description would include include mathematical concepts that are motivated by the study of physics (also known as physical mathematics).

The phrase "mathematical physics" is used in a manner that may be somewhat peculiar at times. Although there are aspects of mathematics that originated from the evolution of physics, these aspects are not, in reality, recognised to be a part of mathematical physics, but other subjects that are closely connected are. For instance, ordinary differential equations and symplectic geometry are often seen as belonging to the realm of purely mathematical sciences, while dynamical systems and Hamiltonian mechanics are considered to be part of the realm of mathematical physics. The phrase "mathematical principles of natural philosophy" was first used as the title of a book written in 1847 by John Herapath. At the time, the book's focus was on "the causes of heat, gaseous elasticity, gravity, and other important phenomena of nature."