The Institute of Physics (IOP) has written a report that examines the relationship between mathematics and physics. |

There is no completely agreed upon definition of mathematical physics, which is closer to mathematics that physics in most respects. The IOP report puts it like this;

Mathematical physics is best described as consisting of two parts: physical research that proceeds primarily through mathematical means and areas of mathematics that work to solve the problems posed by physics.

The Journal of Mathematical Physics define mathematical physics as;

…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.

The IOP booklet looks at a wide range of topics in mathematical physics from quantum mechanics, gravity & black holes, random matrix theory, solitons and topological insulators.

**Link**

Mathematical Physics: What is it and why do we need it?