Occupation Profile for Mathematicians

Conduct research in fundamental mathematics or in application of mathematical techniques to science, management, and other fields. Solve or direct solutions to problems in various fields by mathematical methods.


Significant Points

  • A Ph.D. in mathematics usually is the minimum educational requirement, except in the Federal Government.
  • Master’s degree and Ph.D. holders with a strong background in mathematics and a related field, such as computer science or engineering, should have better employment opportunities in related occupations.
  • Average employment growth is expected for mathematicians.


$86,930.00 Median Annual Wage 0 Average Job Openings Per Year
1.2 Average Unemployment Percentage 0.0 Percentage That Completed High School
3,000 Employment Numbers in 2006 6.1 Percentage That Had Some College
3,000 Employment Numbers in 2016 (est.) 93.3 Percentage That Went Beyond College Degree

Sample Job Titles
Cipher Expert
Computational Physicist
Computational Scientist
Cryptographic Vulnerability Analyst
Emerging Solutions Executive
Engineering Mathematician
Image Scientist
Knowledge Engineer
Numerical Analysis Group Manager
Research Computing Specialist
Research Scientist
Systems Analyst
Systems Engineer
Technical Fellow

  • These occupations often involve coordinating, training, supervising, or managing the activities of others to accomplish goals. Very advanced communication and organizational skills are required. Examples include librarians, lawyers, aerospace engineers, physicists, school psychologists, and surgeons.
  • A bachelor's degree is the minimum formal education required for these occupations. However, many also require graduate school. For example, they may require a master's degree, and some require a Ph.D., M.D., or J.D. (law degree).
  • Extensive skill, knowledge, and experience are needed for these occupations. Many require more than five years of experience. For example, surgeons must complete four years of college and an additional five to seven years of specialized medical training to be able to do their job.
  • Employees may need some on-the-job training, but most of these occupations assume that the person will already have the required skills, knowledge, work-related experience, and/or training.

A Ph.D. degree in mathematics usually is the minimum educational requirement for prospective mathematicians, except in the Federal Government.

Education and training. In the Federal Government, entry-level job candidates usually must have at least a bachelor’s degree with a major in mathematics or 24 semester hours of mathematics courses. Outside the Federal Government, bachelor’s degree holders in mathematics usually are not qualified for most jobs, and many seek advanced degrees in mathematics or a related discipline.

Most colleges and universities offer a bachelor’s degree in mathematics. Courses usually required for this degree include calculus, differential equations, and linear and abstract algebra. Additional courses might include probability theory and statistics, mathematical analysis, numerical analysis, topology, discrete mathematics, and mathematical logic. Many colleges and universities advise or require students majoring in mathematics to take courses in a closely related field, such as computer science, engineering, life science, physical science, or economics. A double major in mathematics and another related discipline is particularly desirable to many employers. High school students who are prospective college mathematics majors should take as many mathematics courses as possible while in high school.

In private industry, candidates for mathematician jobs typically need a Ph.D., although there may be opportunities for those with a master’s degree. Most of the positions designated for mathematicians are in research and development laboratories, as part of technical teams.

In 2007, there were more than 300 graduate programs, offering both master’s and doctoral degrees, in pure or applied mathematics around the country. In graduate school, students conduct research and take advanced courses, usually specializing in a subfield of mathematics.

Other qualifications. For jobs in applied mathematics, training in the field in which mathematics will be used is very important. Mathematics is used extensively in physics, actuarial science, statistics, engineering, and operations research. Computer science, business and industrial management, economics, finance, chemistry, geology, life sciences, and behavioral sciences are likewise dependent on applied mathematics. Mathematicians also should have substantial knowledge of computer programming, because most complex mathematical computation and much mathematical modeling are done on a computer.

Mathematicians need to have good reasoning to identify, analyze, and apply basic principles to technical problems. Communication skills also are important, as mathematicians must be able to interact and discuss proposed solutions with people who may not have extensive knowledge of mathematics.

Advancement. Bachelor’s degree holders who meet State certification requirements may become primary or secondary school mathematics teachers. (For additional information, see the statement on teachers—preschool, kindergarten, elementary, middle, and secondary elsewhere in the Handbook.)

The majority of those with a master’s degree in mathematics who work in private industry do so not as mathematicians but in related fields such as computer science, where they have titles such as computer programmer, systems analyst, or systems engineer.

Nature of Work

Mathematics is one of the oldest and most fundamental sciences. Mathematicians use mathematical theory, computational techniques, algorithms, and the latest computer technology to solve economic, scientific, engineering, physics, and business problems. The work of mathematicians falls into two broad classes—theoretical (pure) mathematics and applied mathematics. These classes, however, are not sharply defined and often overlap.

Theoretical mathematicians advance mathematical knowledge by developing new principles and recognizing previously unknown relationships between existing principles of mathematics. Although these workers seek to increase basic knowledge without necessarily considering its practical use, such pure and abstract knowledge has been instrumental in producing or furthering many scientific and engineering achievements. Many theoretical mathematicians are employed as university faculty, dividing their time between teaching and conducting research.

Applied mathematicians, on the other hand, 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 most efficient way to schedule airline routes between cities, the effects and safety of new drugs, the aerodynamic characteristics of an experimental automobile, or the cost-effectiveness of alternative manufacturing processes.

Applied mathematicians working in industrial research and development may develop or enhance mathematical methods when solving a difficult problem. Some mathematicians, called cryptanalysts, analyze and decipher encryption systems—codes—designed to transmit military, political, financial, or law enforcement-related information.

Applied mathematicians start with a practical problem, envision its separate elements, and then reduce the elements to mathematical variables. They often use computers to analyze relationships among the variables and solve complex problems by developing models with alternative solutions.

Individuals with titles other than mathematician do much of the work in applied mathematics. In fact, because mathematics is the foundation on which so many other academic disciplines are built, the number of workers using mathematical techniques is much greater than the number formally called mathematicians. For example, engineers, computer scientists, physicists, and economists are among those who use mathematics extensively. Some professionals, including statisticians, actuaries, and operations research analysts, are actually specialists in a particular branch of mathematics. (For more information, see the statements on actuaries, operations research analysts, and statisticians elsewhere in the Handbook.) Applied mathematicians are frequently required to collaborate with other workers in their organizations to find common solutions to problems.

Work environment. 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.

Mathematicians who work in academia usually have a mix of teaching and research responsibilities. These mathematicians may conduct research alone or in close collaboration with other mathematicians. Collaborators may work together at the same institution or from different locations, using technology such as e-mail to communicate. Mathematicians in academia also may be aided by graduate students.

Related Occupations

Sources: Career Guide to Industries (CGI), Occupational Information Network (O*Net), Occupation Outlook Handbook (OOH)

Median annual earnings of mathematicians were $86,930 in May 2006. The middle 50 percent earned between $62,970 and $106,250. The lowest 10 percent had earnings of less than $43,500, while the highest 10 percent earned more than $132,190.

In early 2007, the average annual salary for mathematicians employed by the Federal Government in supervisory, nonsupervisory, and managerial positions was $93,539; for mathematical statisticians, $96,121; and for cryptanalysts, the average was $90,435.

For the latest wage information:

The above wage data are from the Occupational Employment Statistics (OES) survey program, unless otherwise noted. For the latest National, State, and local earnings data, visit the following pages:

  • Mathematicians
  • Job Outlook

    Employment of mathematicians is expected to grow as fast as the average. However, keen competition for jobs is expected.

    Employment change. Employment of mathematicians is expected to increase by 10 percent during the 200616 decade, as fast as the average for all occupations. Advancements in technology usually lead to expanding applications of mathematics, and more workers with knowledge of mathematics will be required in the future. However, jobs in industry and government often require advanced knowledge of related scientific disciplines in addition to mathematics. The most common fields in which mathematicians study and find work are computer science and software development, physics, engineering, and operations research. More mathematicians also are becoming involved in financial analysis.

    Job prospects. Job competition will remain keen because employment in this occupation is relatively small and few new jobs are expected. Master’s degree and Ph.D. holders with a strong background in mathematics and a related discipline, such as engineering or computer science, and who apply mathematical theory to real-world problems will have the best job prospects in related occupations.

    Holders of a master’s degree in mathematics will face very strong competition for jobs in theoretical research. Because the number of Ph.D. degrees awarded in mathematics continues to exceed the number of available university positions—especially those that are tenure tracked—many graduates will need to find employment in industry and government.

    Additionally, employment in theoretical mathematical research is sensitive to general economic fluctuations and to changes in government spending. Job prospects will be greatly influenced by changes in public and private funding for research and development.


    Mathematicians held about 3,000 jobs in 2006. Many people with mathematical backgrounds also worked in other occupations. For example, there were about 54,000 jobs as postsecondary mathematical science teachers in 2006.

    Many mathematicians work for Federal or State governments. The U.S. Department of Defense is the primary Federal employer, accounting for about 37 percent of the mathematicians employed by the Federal Government. Many of the other mathematicians employed by the Federal Government work for the National Aeronautics and Space Administration (NASA).

    In the private sector, major employers include scientific research and development services and management, scientific, and technical consulting services. Some mathematicians also work for software publishers, insurance companies, and in aerospace or pharmaceutical manufacturing.

    • Mathematics — Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
    • Engineering and Technology — Knowledge of the practical application of engineering science and technology. This includes applying principles, techniques, procedures, and equipment to the design and production of various goods and services.
    • Sales and Marketing — Knowledge of principles and methods for showing, promoting, and selling products or services. This includes marketing strategy and tactics, product demonstration, sales techniques, and sales control systems.
    • Medicine and Dentistry — Knowledge of the information and techniques needed to diagnose and treat human injuries, diseases, and deformities. This includes symptoms, treatment alternatives, drug properties and interactions, and preventive health-care measures.
    • Physics — Knowledge and prediction of physical principles, laws, their interrelationships, and applications to understanding fluid, material, and atmospheric dynamics, and mechanical, electrical, atomic and sub- atomic structures and processes.
    • Equipment Maintenance — Performing routine maintenance on equipment and determining when and what kind of maintenance is needed.
    • Coordination — Adjusting actions in relation to others' actions.
    • Active Learning — Understanding the implications of new information for both current and future problem-solving and decision-making.
    • Writing — Communicating effectively in writing as appropriate for the needs of the audience.
    • Troubleshooting — Determining causes of operating errors and deciding what to do about it.
    • Near Vision — The ability to see details at close range (within a few feet of the observer).
    • Stamina — The ability to exert yourself physically over long periods of time without getting winded or out of breath.
    • Explosive Strength — The ability to use short bursts of muscle force to propel oneself (as in jumping or sprinting), or to throw an object.
    • Oral Comprehension — The ability to listen to and understand information and ideas presented through spoken words and sentences.
    • Hearing Sensitivity — The ability to detect or tell the differences between sounds that vary in pitch and loudness.
    • Core — Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
    • Core — Assemble sets of assumptions and explore the consequences of each set.
    • Core — Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
    • Core — Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
    • Supplemental — Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
    • Monitoring and Controlling Resources — Monitoring and controlling resources and overseeing the spending of money.
    • Guiding, Directing, and Motivating Subordinates — Providing guidance and direction to subordinates, including setting performance standards and monitoring performance.
    • Assisting and Caring for Others — Providing personal assistance, medical attention, emotional support, or other personal care to others such as coworkers, customers, or patients.
    • Repairing and Maintaining Electronic Equipment — Servicing, repairing, calibrating, regulating, fine-tuning, or testing machines, devices, and equipment that operate primarily on the basis of electrical or electronic (not mechanical) principles.
    • Getting Information — Observing, receiving, and otherwise obtaining information from all relevant sources.
    Related College Curriculum
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