Mathematicians do research in fields such as logic, set theory, abstract algebra, number theory, geometry, topology, dynamical systems, combinatorics, game theory, probability, and statistics. Although math has numerous applications, mathematicians also find math interesting in its own right.

The mathematics required for mathematicians includes but is not limited to College Algebra, Trigonometry, Calculus I, II, and III, Linear Algebra, Ordinary Differential Equations, Real Analysis, Abstract Algebra, Theory of Analysis, and Complex Analysis. This is a very basic list; most mathematicians will study all the math they can and will study additional topics depending on their interests.

In order to find the average income of a mathematician, please use this link.

For more information about mathematicians, the US Bureau of Labor Statistics breaks down the job of a mathematician into multiple sections to help better understand the requirements of becoming a mathematician.