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.
Significant
points
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.
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 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.
Working
conditions
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
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
school.
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.
Employment
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.
Job
outlook
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 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 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.
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.
Earnings
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.
Related
occupations
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.
Suggested
citation
Bureau of Labor Statistics, U.S. Department of Labor, Occupational
Outlook Handbook, 2006-07 Edition, Mathematicians, on the Internet
at
http://www.bls.gov/oco/ocos043.htm
(visited July 18, 2007).