A professional who conducts research in fundamental mathematics and in application of mathematical techniques to science, management, and other fields, and solves or directs solutions to problems in various fields by mathematical methods. Responsibilities include:

• Conducts research in such branches of mathematics as algebra, geometry, number theory, logic, and topology, and studies and tests hypotheses and alternative theories.
• Conceives and develops ideas for application of mathematics to wide variety of fields, including science, engineering, military planning, electronic data processing, and management.
• Applies mathematics or mathematical methods to solution of problems in research, development, production, logistics, and other functional areas, utilizing knowledge of subject or field to which applied, such as physics, engineering, astronomy, biology, economics, business and industrial management, or cryptography.
• Performs computations, applies methods of numerical analysis, and operates or directs operation of desk calculators and mechanical and electronic computation machines, analyzers, and plotters in solving problems in support of mathematical, scientific, or industrial research activity.
• Acts as advisor or consultant to research personnel concerning mathematical methods and applications.
• May be designated according to function as Mathematician, Applied; Mathematician, Research.