A Ph.D. degree in mathematics usually is the minimum educational
requirement, except in the Federal Government.
The number of jobs with the title “mathematician” is declining
as the workforce becomes increasingly specialized; competition
will be keen for the limited number of available jobs.
Master’s 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.
Nature of the 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, 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
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 actuaries,
operations research analysts, and statisticians elsewhere in the
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.
Training, Other Qualifications, and Advancement
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 major—24
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 master’s 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 bachelor’s or 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.
A bachelor’s 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
In 2004, about 200 colleges and universities offered a master’s
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
“mathematician.” As a result, competition is expected to be keen
for the limited number of jobs as mathematicians. Master’s 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
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
Private industry jobs require at least a master’s degree in mathematics
or in a related field. Bachelor’s degree holders in mathematics
usually are not qualified for most jobs, and many seek advanced
degrees in mathematics or a related discipline. However, 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.)
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 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.
Other occupations that require extensive knowledge of mathematics
or, in some cases, a degree in mathematics include actuaries,
statisticians, computer programmers, computer systems analysts,
computer scientists and database administrators, computer software
engineers, and operations research analysts. A strong background
in mathematics also facilitates employment as teachers—postsecondary;
teachers—preschool, kindergarten, elementary, middle, and secondary;
engineers; economists; market and survey researchers; financial
analysts and personal financial advisors; and physicists and astronomers.
Sources of Additional Information
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 Government’s 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.
Source: Bureau of Labor
Statistics, U.S. Department of Labor, Occupational
Outlook Handbook, 2006-07 Edition,