People who specialize in mathematics which is their main field of study are called mathematicians. Mathematicians are concerned with logic, transformations, numbers and general ideas which cover all these mathematical concepts. Excelling in mathematics requires clear conceptual understanding, remembering all correct formulae and continuous and regular practise. The world has seen several great and genius mathematicians who gave various postulates and theorems which are used while solving mathematical problems. Some scientists are considered mathematicians if their work provides insight into mathematics.
A classic example of such a famous scientist is Sir Isaac Newton. Mathematicians whose research provides insight into other fields of research are called applied mathematicians.
E.T. Bell had once remarked, “Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.”