Mathematics is one of the oldest and most basic sciences. Mathematicians today are engaged in a wide variety of activities, ranging from the creation of new mathematical theories and techniques involving the latest technology to the solving of economic, scientific, engineering, and business problems using mathematical knowledge and computational tools.

Mathematical work falls into two broad classes: Theoretical (pure) mathematics; and applied mathematics. However, these classes are not sharply defined and often overlap.

Theoretical mathematicians advance mathematical science by developing new principles and new relationships between existing principles of mathematics. Although they seek to increase basic knowledge without necessarily considering its practical use, this pure and abstract knowledge has been instrumental in producing or furthering many scientific and engineering achievements.

Applied mathematicians use theories and techniques, such as mathematical modeling and computational methods, to formulate and solve practical problems in business, government, engineering, and the physical, life, and social sciences. For example, they may analyze the mathematical aspects of computer and communications networks, the effects of new drugs on disease, the aerodynamic characteristics of aircraft, or the distribution costs or manufacturing processes of businesses. Applied mathematicians working in industrial research and development may develop or enhance mathematical methods when confronted with difficult problems. Some mathematicians, called cryptanalysts, analyze and decipher encryption systems designed to transmit national security-related information.

Mathematicians use computers extensively to analyze relationships among variables, solve complex problems, develop models, and process large amounts of data.

Much work in applied mathematics, however, is carried on by persons other than mathematicians. In fact, because mathematics is the foundation upon which many other academic disciplines are built, the number of workers using mathematical techniques is many times greater than the number actually designated as mathematicians. Engineers, computer scientists, and economists are among those who use mathematics extensively but have job titles other than mathematician. Some workers, such as statisticians, actuaries, and operations research analysts, actually are specialists in a particular branch of mathematics. (See statements on actuaries, operations research analysts, and statisticians elsewhere in the Handbook.)

Applied mathematicians often use their knowledge to solve practical problems in business, government, engineering, and science.

Mathematicians working for government agencies or private firms usually have structured work schedules. They may work alone, in a small group of mathematicians, or as an integral part of a team that includes engineers, computer scientists, physicists, technicians, and others. Deadlines, overtime work, special requests for information or analysis, and travel to attend seminars or conferences may be part of their jobs.

Mathematics faculty have flexible work schedules, dividing their time among teaching, research, consulting, and administrative responsibilities.

Mathematicians held about 16,000 jobs in 1992. In addition, about 16,000 persons held mathematics faculty positions in colleges and universities, according to the American Mathematical Society. (See the statement on college and university faculty elsewhere in the Handbook.)

Most nonfaculty mathematicians work in the government and in service and manufacturing industries. The Department of Defense is the primary Federal employer of mathematicians; more than three-fourths of the mathematicians employed by the Federal Government work for the Navy, Army, or Air Force. A significant number of mathematicians also work in State governments. In the private sector, major employers within services industries include research and testing services, educational services, and computer and data processing services. Within manufacturing, the aircraft, chemicals, and computer and office equipment industries are key employers. Some mathematicians also work for banks, insurance companies, and public utilities.

A bachelor's degree in mathematics is the minimum education needed for prospective mathematicians. A master's degree in mathematics is sufficient preparation for some research positions and for teaching jobs in many junior or community colleges and in some small 4-year colleges. However, in most 4-year colleges and universities, as well as in many research and development positions in private industry, a doctoral degree is necessary.

In the Federal Government, entry-level job candidates usually must have a 4-year degree with a major in mathematics or a 4-year degree with the equivalent of a mathematics major 24 semester hours of mathematics courses.

In private industry, job candidates generally need a master's degree to obtain jobs as mathematicians. The majority of bachelor's and master's degree holders in private industry work, not as mathematicians, but in related fields such as computer science, where they are called computer programmers, systems analysts, or systems engineers.

A bachelor's degree in mathematics is offered by most colleges and universities. Mathematics courses usually required for this degree are calculus, differential equations, and linear and abstract algebra. Additional coursework might include probability theory and statistics, mathematical analysis, numerical analysis, topology, modern algebra, discrete mathematics, and mathematical logic. Many colleges and universities urge or even require students majoring in mathematics to take several courses in a field that uses or is closely related to mathematics, such as computer science, engineering, operations research, a physical science, statistics, or economics. A double major in mathematics and either computer science, statistics, or one of the sciences is particularly desirable. A prospective college mathematics major should take as many mathematics courses as possible while in high school.

In 1992, 255 colleges and universities offered a master's degree as the highest degree in either pure or applied mathematics; 187 offered a Ph.D. in pure or applied mathematics. In graduate school, students conduct research and take advanced courses, usually specializing in a subfield of mathematics. Some areas of concentration are algebra, number theory, real or complex analysis, geometry, topology, logic, and applied mathematics.

For work in applied mathematics, training in the field in which the mathematics will be used is very important. Fields in which applied mathematics is used extensively include physics, actuarial science, engineering, and operations research; of increasing importance are computer and information science, business and industrial management, economics, statistics, chemistry, geology, life sciences, and the behavioral sciences.

Mathematicians should have substantial knowledge of computer programming because most complex mathematical computation and much mathematical modeling is done by computer.

Mathematicians need good reasoning ability and persistence in order to identify, analyze, and apply basic principles to technical problems. Communication skills are also important, as mathematicians must be able to interact with others, including nonmathematicians, and discuss proposed solutions to problems.

Employment of mathematicians is expected to increase more slowly than the average for all occupations through the year 2005. The number of jobs available for workers whose educational background is solely mathematics is not expected to increase significantly. Many firms engaged in civilian research and development that use mathematicians are not planning to expand their research departments much, and, in some cases, may reduce them. Expected reductions in defense-related research and development will also affect mathematicians' employment, especially in the Federal Government. Those whose educational background includes the study of a related discipline will have better job opportunities. However, as advancements in technology lead to expanding applications of mathematics, more workers with a knowledge of mathematics will be required. An increasing number of these workers have job titles which reflect the end product of their work rather than the discipline of mathematics used in that work, which will contribute further to the slowdown in positions for mathematicians.

Bachelor's degree holders in mathematics are usually not qualified for jobs as mathematicians. However, those with a strong background in computer science, electrical or mechanical engineering, or operations research should have good opportunities in industry. Bachelor's degree holders who meet State certification requirements may become high school mathematics teachers. (For additional information, see the statement on kindergarten, elementary, and secondary school teachers elsewhere in the Handbook.)

Holders of a master's degree in mathematics will face very strong competition for jobs in college teaching or theoretical research. However, job opportunities in applied mathematics and related areas such as computer programming, operations research, and engineering design in industry and government will be more numerous.

According to a 1992 College Placement Council Survey, starting salary offers for mathematics graduates with a bachelor's degree averaged about $28,400 a year; for those with a master's degree, $33,600; and for new doctoral graduates, $41,000. Starting salaries were generally higher in industry and government than in educational institutions. For example, the American Mathematical Society reported that, based on a 1992 survey, median annual earnings for new recipients of doctorates in research were $30,200; for those in teaching or teaching and research (9-10 month academic year), $34,000; for those in government, $53,000; and for those in business and industry, $53,000.

In the Federal Government in 1993, the average annual salary for mathematicians in supervisory, nonsupervisory, and managerial positions was $53,232; for mathematical statisticians, $54,109; and for cryptanalysts, $43,070.

Benefits for mathematicians tend to be similar to those offered to most professionals who work in office settings: Vacation and sick leave, health and life insurance, and a retirement plan, among others.

Other occupations that require a degree in or extensive knowledge of mathematics include actuary, statistician, computer programmer, systems analyst, systems engineer, and operations research analyst. In addition, a strong background in mathematics facilitates employment in fields such as engineering, economics, finance, and physics.

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* Reprinted with Permission of U. S. Department of Labor*