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Mathematicians

(D.O.T.  020.067-014, .167-030; 199.267-014)

Nature of the Work

Mathematics is one of the oldest and most basic sciences.
Mathematicians today are engaged in a wide variety of activities,
ranging from the creation of new mathematical theories and
techniques involving the latest technology to the solving of
economic, scientific, engineering, and business problems using
mathematical knowledge and computational tools.

   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 or
furthering many scientific and engineering achievements.

   Applied mathematicians 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 mathematical aspects of computer and communications
networks, the effects of new drugs on disease, the aerodynamic
characteristics of aircraft, or the distribution costs or
manufacturing processes of businesses.  Applied mathematicians
working in industrial research and development may develop or
enhance mathematical methods when confronted with difficult
problems.  Some mathematicians, called cryptanalysts, analyze and
decipher encryption systems designed to transmit national
security-related information.

   Mathematicians use computers extensively to analyze relationships
among variables, solve complex problems, develop models, and process
large amounts of data.

   Much work in applied mathematics, however, is carried on by persons
other than mathematicians.  In fact, because mathematics is the
foundation upon which many other academic disciplines are built, the
number of workers using mathematical techniques is many times
greater than the number actually designated as mathematicians.
Engineers, computer scientists, and economists are among those who
use mathematics extensively but have job titles other than
mathematician.  Some workers, such as statisticians, actuaries, and
operations research analysts, actually are specialists in a
particular branch of mathematics.  (See statements on actuaries,
operations research analysts, and statisticians elsewhere in the
Handbook.)

   Applied mathematicians often use their knowledge to solve practical
problems in business, government, engineering, and science.

Working Conditions

Mathematicians working for government agencies or private firms
usually have structured work schedules.  They may work alone, in a
small group of mathematicians, or as an integral part of a team that
includes engineers, computer scientists, physicists, technicians,
and others.  Deadlines, overtime work, special requests for
information or analysis, 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 16,000 jobs in 1992.  In addition, about
16,000 persons held mathematics faculty positions in colleges and
universities, according to the American Mathematical Society.  (See
the statement on college and university faculty elsewhere in the
Handbook.)

   Most nonfaculty mathematicians work in the government and in service
and manufacturing industries.  The Department of Defense is the
primary Federal employer of mathematicians; more than three-fourths
of the mathematicians employed by the Federal Government work for
the Navy, Army, or Air Force.  A significant number of
mathematicians also work in State governments.  In the private
sector, major employers within services industries include research
and testing services, educational services, and computer and data
processing services.  Within manufacturing, the aircraft, chemicals,
and computer and office equipment industries are key employers.
Some mathematicians also work for banks, insurance companies, and
public utilities.

Training, Other Qualifications, and Advancement

A bachelor's degree in mathematics is the minimum education needed
for prospective mathematicians.  A master's degree in mathematics is
sufficient preparation for some research positions and for teaching
jobs in many junior or community colleges and in some small 4-year
colleges.  However, in most 4-year colleges and universities, as
well as in many research and development positions in private
industry, a doctoral degree is necessary.

   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, job candidates generally need a master's degree
to obtain jobs as mathematicians.  The majority of bachelor's and
master's degree holders in private industry work, not as
mathematicians, but in related fields such as computer science,
where they are called computer programmers, systems analysts, or
systems engineers.

   A bachelor's degree in mathematics is offered by most colleges and
universities.  Mathematics courses usually required for this degree
are calculus, differential equations, and linear and abstract
algebra.  Additional coursework might include probability theory and
statistics, mathematical analysis, numerical analysis, topology,
modern algebra, discrete mathematics, and mathematical logic.  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,
engineering, operations research, a physical science, statistics, or
economics.  A double major in mathematics and either computer
science, statistics, or one of the sciences is particularly
desirable.  A prospective college mathematics major should take as
many mathematics courses as possible while in high school.

   In 1992, 255 colleges and universities offered a master's degree as
the highest degree in either pure or applied mathematics; 187
offered a Ph.D.  in pure or applied mathematics.  In graduate
school, students conduct research and take advanced courses, usually
specializing in a subfield of mathematics.  Some areas of
concentration are algebra, number theory, real or complex analysis,
geometry, topology, logic, and applied mathematics.

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

   Mathematicians should have substantial knowledge of computer
programming because most complex mathematical computation and much
mathematical modeling is done by computer.

   Mathematicians need good reasoning ability and persistence in order
to identify, analyze, and apply basic principles to technical
problems.  Communication skills are also important, as
mathematicians must be able to interact with others, including
nonmathematicians, and discuss proposed solutions to problems.

Job Outlook

Employment of mathematicians is expected to increase more slowly
than the average for all occupations through the year 2005.  The
number of jobs available for workers whose educational background is
solely mathematics is not expected to increase significantly.  Many
firms engaged in civilian research and development that use
mathematicians are not planning to expand their research departments
much, and, in some cases, may reduce them.  Expected reductions in
defense-related research and development will also affect
mathematicians' employment, especially in the Federal Government.
Those whose educational background includes the study of a related
discipline will have better job opportunities.  However, as
advancements in technology lead to expanding applications of
mathematics, more workers with a knowledge of mathematics will be
required.  An increasing number of these workers have job titles
which reflect the end product of their work rather than the
discipline of mathematics used in that work, which will contribute
further to the slowdown in positions for mathematicians.

   Bachelor's degree holders in mathematics are usually not qualified
for jobs as mathematicians.  However, those with a strong background
in computer science, electrical or mechanical engineering, or
operations research should have good opportunities in industry.
Bachelor's degree holders who meet State certification requirements
may become high school mathematics teachers.  (For additional
information, see the statement on kindergarten, elementary, and
secondary school teachers elsewhere in the Handbook.)

   Holders of a master's degree in mathematics will face very strong
competition for jobs in college teaching or theoretical research.
However, job opportunities in applied mathematics and related areas
such as computer programming, operations research, and engineering
design in industry and government will be more numerous.

Earnings

According to a 1992 College Placement Council Survey, starting
salary offers for mathematics graduates with a bachelor's degree
averaged about $28,400 a year; for those with a master's degree,
$33,600; and for new doctoral graduates, $41,000.  Starting salaries
were generally higher in industry and government than in educational
institutions.  For example, the American Mathematical Society
reported that, based on a 1992 survey, median annual earnings for
new recipients of doctorates in research were $30,200; for those in
teaching or teaching and research (9-10 month academic year),
$34,000; for those in government, $53,000; and for those in business
and industry, $53,000.

   In the Federal Government in 1993, the average annual salary for
mathematicians in supervisory, nonsupervisory, and managerial
positions was $53,232; for mathematical statisticians, $54,109; and
for cryptanalysts, $43,070.

   Benefits for mathematicians tend to be similar to those offered to
most professionals who work in office settings: Vacation and sick
leave, health and life insurance, and a retirement plan, among
others.

Related Occupations

Other occupations that require a degree in or extensive knowledge of
mathematics include actuary, statistician, computer programmer,
systems analyst, systems engineer, and operations research analyst.
In addition, a strong background in mathematics facilitates
employment in fields such as engineering, economics, finance, and
physics.

Sources of Additional Information

   For more information about the field of mathematics, including
career opportunities and professional training, contact:

   American Mathematical Society, P.O.  Box 6248, Providence, RI 02940.

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

   For specific information on careers in applied mathematics, contact:

   Society for Industrial and Applied Mathematics, 3600 University City
Science Center, Philadelphia, PA 19104-2688.

   For information about careers in noncollegiate academic
institutions, contact:

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

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