Mathematics is a formal science that, from axioms through logical reasoning, has as its object of study the properties and relationships between abstract entities such as numbers, geometric figures or symbols, while physics is the science that studies the properties and characteristics of bodies, as well as the laws that govern the changes that affect their state and their movement, without modifying their nature.
In many of these fields mathematical physicists have developed theorems and have demonstrated general properties to which certain theories that have served to reformulate physical models lead. In mathematical physics, working methods are generally closer to the deductive method used in mathematics than to the more typical inductive methods of experimental physics. Sometimes the use of the term "mathematical physics" is idiosyncratic. While certain parts of mathematics that were initially developed from physics are not considered elements of mathematical physics, some other closely related fields are.
Historically many areas of mathematics were developed by the stimulus provided by physical problems. Thus, for example, differential calculus and differential equations acquired great interest after they were used by Newton in the formulation of Newton's famous laws. The variational calculation began with the attempt to solve certain physical problems such as the problem of the brachistocrona raised in the late seventeenth century.