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 many scientific and engineering achievements. For example, in 1854, G.F.B. Reimann invented a seemingly impractical non-Euclidian geometry that was to become part of Albert Einstein's theory of relativity. Years later, this theory contributed to the creation of atomic power.

Applied mathematicians use mathematics to develop theories, techniques, and approaches to solve practical problems in career, government, engineering, and the natural and social sciences. Their work ranges from analysis of the mathematical aspects of launching communications satellites to studies of the effects of new drugs on disease.

Much work in applied mathematics, however, is carried on by persons other than mathematicians. In fact, the number of workers using mathematical techniques is many time greater than the number actually designated as mathematicians.

Working Conditions

Mathematicians working for government agencies and private firms have structured work schedules. They may work alone with only computers, calculators, and mathematical formulas as company. Or they may be an integral part of a research team that includes engineers, computer scientists, and others. Deadlines, overtime work, special requests for information, 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.

Employment

Mathematicians held about 18,000 jobs in 1990. In addition, about 33,000 persons held mathematics faculty positions in colleges and universities.

Most mathematicians working in the government--primarily Federal--and in service and manufacturing industries. The department of Defense and the National Aeronautics and Space Administration are the primary employers of mathematicians working in the Federal Government. Major employers within the services sector were miscellaneous career services, including research and development laboratories; educational services; and noncommercial educational and research organizations. Within manufacturing, guided missiles and space vehicles; aircraft; and office, computing, and accounting machine industries provided the most jobs.

Mathematicians work in all States but are concentrated in those with high-technology industries.

Training, Other Qualifications, and Advancement

An advanced degree is the preferred requirement for beginning teaching jobs, as well as for most research positions. However, in most 4-year colleges and universities, the Ph.D. degree is necessary for full faculty status. The master's degree is generally the minimum requirement for teaching jobs in 2-year and small 4-year colleges.

A bachelor's degree is considered adequate preparation for some jobs in private industry and government. Individuals with this background usually assist senior mathematicians by performing computations and solving less advanced problems in applied mathematics. The majority of bachelor's degree holders work in related fields such as computer science where employment opportunities are rapidly expanding. However, an advanced degree is a prerequisite for the more responsible positions. Many research positions require the doctorate.

The bachelor's degree in mathematics is offered by most colleges and universities. Mathematics courses usually required for a degree are analytical geometry, calculus, differential equations, linear algebra, probability theory and statistics, mathematical analysis, and modern algebra. 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 or mathematics and statistics is particularly desirable. A prospective college mathematics student should take as many mathematics courses as possible while in high school.

About 470 colleges and universities offer the master's degree in mathematics; nearly 200 also offer the Ph.D. In graduate school, students conduct research and take advanced courses, usually in a specific field of mathematics such as algebra, mathematical analysis, or geometry.

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, career and industrial management, economics, statistics, chemistry and life sciences, and the behavioral sciences.

Mathematicians should have a working knowledge of computer programming since most complex mathematical computation is done by computer.

Mathematicians need good reasoning ability, persistence, and the ability to apply basic principles to new types of problems. They must be able to communicate well since they often need to discuss the problem to be solved with non-mathematicians.

Job Outlook

Employment of mathematicians is expected to increase about as fast as the average for all occupations through the year 2000. Most job openings, however, will arise from the need to replace experienced mathematicians who transfer to other occupations, retire, or leave the labor force for other reasons.

The shortage of Ph.D.'s in mathematics is expected to continue, resulting in favorable employment opportunities. In industry, holders of the doctorate in applied mathematics have better employment prospects than their theoretically oriented colleagues. Holders of the doctorate in theoretical mathematics should continue to have good opportunities for teaching and research jobs in colleges and universities.

Industry and government agencies will need mathematicians for work in operations research, mathematical modeling, numerical analysis, computer systems design and programming, information and data processing, applied mathematical physics, robotics, market research, commercial surveys, and as consultants in industrial laboratories.

Holders of a master's degree in mathematics may have difficulty finding a job in college teaching or theoretical research. However, there will be many openings in applied areas such as computer science and data processing.

Bachelor's degree holders in mathematics with a strong background--preferably a double major--in computer science should have very good opportunities in computerized data processing activities in industry. Those who meet State certification requirements may become high school mathematics teachers, who are currently in short supply.

Earnings

According to a 1990 College Placement Council Survey, starting salary offers for mathematics graduates with a bachelor's degree averaged about $28,600 a year; for those with a master's degree, $30,800; and for new graduates having the Ph.D., $42,325. Starting salaries were generally higher in industry than in government or educational institutions.

According to the Professional Scientific Personnel Report, 15th edition, experienced mathematicians averaged from $36,712 to $71,750 a year.

Fringe benefits for mathematicians tend to be similar to those offered to most professional who work in office settings; vacation and sick leave, health and life insurance, and retirement plans, among others.

Related Occupations

A degree in mathematics generally qualifies one to enter related occupations such as actuarial scientist, statistician, computer programer, systems analyst, and operations research analyst. In addition, a strong background in mathematics facilitates employment in fields such as engineering, economics, finance, and genetics.

Sources of Additional Information

Several brochures are available that give facts about the field of mathematics, including career opportunities, professional training, and colleges and universities with degree programs.

Seeking Employment in the Mathematical Sciences is available for $2, and $2 for additional pairs of copies, from:

American Mathematical Society, P.O. Box 6248, Providence, R.I. 02940.

Professional Opportunities in Mathematics is available for $1.50 from:

Mathematical Association of America, 1529 18th St. NW., Washington, D.C. 20036.

For specific information on careers in applied mathematics, contact:

Society for Industrial and Applied Mathematics, 1405 Architects Building, 117 S. 17th St., Philadelphia, PA 19103.

For information on a career as a mathematical statistician, contact:

Institute of Mathematical Statistics, 3401 Investment Blvd., No. 7, Hayward, California 94545.

Information on Federal job opportunities is available from area offices of the State employment service and the U.S. Office of Personnel Management or from the Federal Job Information Centers located in various large cities throughout the country.

For information about careers in noncollegiate academic institutions, contact:

National Council of Teachers of Mathematics, 1906 Association Dr., Reston, VA 22091.