A mathematician is a person with an extensive knowledge of mathematics who use this knowledge in their

work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, collection, quantity, structure, space, and change.

Mathematicians involved with solving problems outside of pure mathematics are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, and localized constructs, applied mathematicians work regularly in the study and formulation of mathematical models.

The discipline of applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics" is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on problems, often concrete but sometimes abstract. As professionals focused on problem solving, applied mathematicians look into the formulation, study, and use of mathematical models in science, engineering, business, and other areas of mathematical practice.