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A mathematician solves or directs the solution of problems in higher mathematics, including algebra, geometry, number theory, logic, and topology. Theoretical mathematicians work with the relationships among mathematical forms and the underlying principles that can be applied to problems, including electronic data processing and military planning. Applied mathematicians develop the techniques and approaches to problem solving in the physical, biological, and social sciences. Approximately 3,030 mathematicians are employed in nonacademic settings in the United States.