Other important mathematical physicists of the seventeenth century included the Dutchman Christiaan Huygens (famous for suggesting the wave theory of light), and the German Johannes Kepler ( Tycho Brahe's assistant, and discoverer of the equations for planetary motion/orbit). The great seventeenth century English physicist and mathematician, Isaac Newton, developed a wealth of new mathematics (for example, calculus and several numerical methods (most notably Newton's method) to solve problems in physics. Other notable mathematical physicists at the time included Abū Rayhān al-Bīrūnī and Al-Khazini, who introduced algebraic and fine calculation techniques into the fields of statics and dynamics. His conceptions of mathematical models and of the role they play in his theory of sense perception, as seen in his Book of Optics (1021), laid the foundations for mathematical physics. One of the earliest mathematical physicists was the eleventh century Iraqi physicist and mathematician, Ibn al-Haytham, known in the West as Alhazen. For example, ordinary differential equations and symplectic geometry are generally viewed as purely mathematical disciplines, whereas dynamical systems and Hamiltonian mechanics belong to mathematical physics. Certain parts of mathematics that initially arose from the development of physics are not considered parts of mathematical physics, while other closely related fields are. The usage of the term 'Mathematical physics' is sometimes idiosyncratic.
Statistical mechanics forms a separate field, which is closely related with the more mathematical ergodic theory and some parts of probability theory. This was, however, gradually supplemented by topology in the mathematical description of cosmological as well as quantum field theory phenomena. This was group theory: and it played an important role in both quantum field theory and differential geometry. The special and general theories of relativity require a rather different type of mathematics.
These constitute the mathematical basis of another branch of mathematical physics. The theory of atomic spectra (and, later, quantum mechanics) developed almost concurrently with the mathematical fields of linear algebra, the spectral theory of operators, and more broadly, functional analysis. Physical applications of these developments include hydrodynamics, celestial mechanics, elasticity theory, acoustics, thermodynamics, electricity, magnetism, and aerodynamics. These were developed intensively from the second half of the eighteenth century (by, for example, D'Alembert, Euler, and Lagrange) until the 1930s. The theory of partial differential equations (and the related areas of variational calculus, Fourier analysis, potential theory, and vector analysis) are perhaps most closely associated with mathematical physics. There are several distinct branches of mathematical physics, and these roughly correspond to particular historical periods.
This definition does, however, not cover the situation where results from physics are used to help prove facts in abstract mathematics which themselves have nothing particular to do with physics. A very typical definition is the one given by the Journal of Mathematical Physics: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories." There is no real consensus about what does or does not constitute mathematical physics.
Mathematical physics is the scientific discipline concerned with the interface of mathematics and physics.