A mathematician is a person whose primary area of study and research is mathematics. In other words, a mathematician is a person who contributes to the field of mathematics. People who apply mathematics to other fields, but do not contribute directly to mathematics, are generally not considered mathematicians.

Overview

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Unlike the other sciences, fundamental research in much of mathematics does not consist of performing experiments. Rather, mathematics is about problem-solving, where truths are deduced from other known truths. Computer experiments and other numerical evidence can result in new problems and are sometimes used to solve them, though most of the time they are just used as indicators that the work is on the right track - numerical evidence is not proof to a mathematician. In the end mathematics research is about constructing proofs of theorems, and most journals would reject a paper consisting solely of numerical data. Some outstanding open problems in mathematics, such as the Birch and Swinnerton-Dyer conjecture, developed after analyzing numerical work on a computer.

Not only is calculation not a big part of some areas of mathematics research, but people who have had an important influence on mathematics do not necessarily have any extraordinary ability in adding or multiplying numbers. For instance, Albert Einstein, whose ideas had a significant impact in geometry, had great difficulties with mathematics when he was a youth. See mental calculators to read about prodigies performing impressive mental calculations.

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