Mathematics is the study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. Mathematicians use tools such as mathematical theory, well-defined procedures called algorithms, and the latest computer technology to solve economic, scientific, engineering, physics, and business problems.

Mathematicians usually work in comfortable offices. They often are part of interdisciplinary teams that may include economists, engineers, computer scientists, physicists, technicians, and others.

Deadlines, overtime work, special requests for information or analysis, and prolonged travel to attend seminars or conferences may be part of their jobs.

Mathematics is divided into two areas: theoretical, or pure, mathematics, and applied mathematics. However, these two areas often overlap.

Mathematicians working in theoretical mathematics are concerned with expanding and clarifying mathematical theories and laws. They seek to increase basic knowledge about mathematical relationships and formulate new laws of mathematics.

Although the few mathematicians in theoretical research do not consider the practical uses of their findings, their work has been essential in many areas of science and engineering. For example, a new kind of geometry developed in the 1850s formed part of the basis for the theory of relativity, which in turn made the development of nuclear energy possible.

Mathematicians doing applied work use the theories and laws developed by theoretical mathematicians.

Applied mathematicians solve specific problems in such fields as physical science, social science, business, computer science, government, biology, and engineering. They may work in the electronics industry developing new kinds of computers and software. Applied mathematicians sometimes study numerical information about medical problems, such as the effect of a new drug on a disease.

Mathematicians working in the aerospace field may provide calculations that help determine whether the outside surfaces of a spaceship are properly designed to keep it on course.

Although mathematicians work in many different fields and apply their work in a variety of ways, they all use numbers. Mathematicians take abstract ideas or specific problems and put them into numerical form. They use computers regularly, as well as more traditional computational devices such as slide rules and calculators.

About three-quarters of all mathematicians are employed by colleges and universities. Most of these mathematicians teach, but some also do research. Other mathematicians work for private companies in industries such as aerospace, communications, and electrical equipment manufacturing. Most mathematicians who work for the federal government are involved in space or defense-related projects. Many workers who are not considered mathematicians use mathematical techniques extensively. Statisticians, actuaries, systems analysts, computer programmers, and mathematics teachers all use mathematics.