A Ph.D. degree in mathematics usually is the minimum educational requirement, except in the Federal Government.
The number of jobs with the title ďmathematicianĒ is declining as the workforce becomes increasingly specialized;
competition will be keen for the limited number of available jobs.
Masterís and Ph.D. degree 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.
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 classestheoretical (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. (See the statement on teacherspostsecondary elsewhere in the Handbook.)
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,
and engineering and in 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 designed to transmit military, political, financial, or law enforcement-related information in code.
Applied mathematicians start with a practical problem, envision the separate elements of the process
under consideration, 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.
Much of the work in applied mathematics is done by individuals with titles other than mathematician.
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 designated
as 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, actually are specialists in a particular branch of mathematics.
Frequently, applied mathematicians are required to collaborate with other workers in their
organizations to achieve common solutions to problems. (For more information, see the statements on
operations research analysts, and
statisticians elsewhere in the Handbook.)
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.
A Ph.D. degree in mathematics usually is the minimum educational requirement for prospective
mathematicians, except in the Federal Government. 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 major24 semester hours of mathematics courses.
In private industry, candidates for mathematician jobs typically need a Ph.D., although
there may be opportunities for those with a masterís degree. Most of the positions designated
for mathematicians are in research and development laboratories, as part of technical teams.
In such settings, mathematicians engage either in basic research on pure mathematical principles
or in applied research on developing or improving specific products or processes. The majority
of those with a bachelorís or masterís 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.
A bachelorís degree in mathematics is offered by most colleges and universities.
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 urge or require
students majoring in mathematics to take courses in a field that is closely related
to mathematics, 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 2004, about 200 colleges and universities offered a masterís degree as the highest
degree in either pure or applied mathematics; about 200 offered a Ph.D. degree in pure or
applied mathematics. In graduate school, students conduct research and take advanced courses,
usually specializing in a subfield of mathematics.
For jobs in applied mathematics, training in the field in which the 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 good reasoning ability and persistence 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.
Mathematicians held about 2,500 jobs in 2004. Many people with mathematical
backgrounds also worked in other occupations. For example, about 53,000 persons held
positions as postsecondary mathematical science teachers in 2004.
Many mathematicians work for Federal or State governments. The U.S. Department of Defense
is the primary Federal employer, accounting for about three-fourths 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.
Employment of mathematicians is expected to decline through 2014, reflecting
the reduction in the number of jobs with the title ďmathematician.Ē As a result, competition is expected to
be keen for the limited number of jobs as mathematicians. Masterís and Ph.D. degree holders with a strong
background in mathematics and a related discipline, such as engineering or computer science, should have
the best opportunities. Many of these workers have job titles that reflect their occupation, such as
systems analyst, rather than the title mathematician, reflecting their primary educational background.
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. Mathematicians must compete for jobs, however,
with people who have degrees in these other disciplines. The most successful jobseekers will
be able to apply mathematical theory to real-world problems and will possess good communication, teamwork, and computer skills.
Private industry jobs require at least a masterís degree in mathematics or in a related field.
Bachelorís degree holders in mathematics usually are not qualified for most jobs, and many seek
advanced degrees in mathematics or a related discipline. However, bachelorís degree holders who
meet State certification requirements may become primary or secondary school mathematics teachers.
(For additional information, see the statement on teacherspreschool, kindergarten,
elementary, middle, and secondary elsewhere in the Handbook.)
Holders of a masterís 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 university positions available, many of these graduates will need to find
employment in industry and government.
Median annual earnings of mathematicians were $81,240 in May 2004. The middle 50 percent earned between $60,050 and $101,360.
The lowest 10 percent had earnings of less than $43,160, while the highest 10 percent earned over $120,900.
In early 2005, the average annual salary for mathematicians employed by the Federal Government in supervisory,
nonsupervisory, and managerial positions was $88,194; that for mathematical statisticians was $91,446; and for cryptanalysts the average was $70,774.
For more information about careers and training in mathematics, especially for doctoral-level employment, contact:
American Mathematical Society, 201 Charles St., Providence, RI 02904-2294. Internet: http://www.ams.org
For specific information on careers in applied mathematics, contact:
Society for Industrial and Applied Mathematics, 3600 University City Science Center, Philadelphia, PA 19104-2688.
Information on obtaining positions as mathematicians with the Federal Government is available from the
Office of Personnel Management through USAJOBS, the Federal Governmentís official employment information system.
This resource for locating and applying for job opportunities can be accessed through the
Internet at http://www.usajobs.opm.gov or through an interactive
voice response telephone system at (703) 724-1850 or TDD (978) 461-8404. These numbers are not tollfree, and charges may result.
Bureau of Labor Statistics, U.S. Department of Labor, Occupational Outlook Handbook, 2006-07 Edition,
Mathematicians, on the Internet at
(visited June 21, 2006).