• 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, 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 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 they solve complex problems by developing models with alternative solutions.
• Individuals with titles other than mathematician also do 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.
• Applied mathematicians frequently are required to collaborate with other workers in their organizations to find common solutions to problems.

• 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. Many mathematicians also are involved in financial analysis and in life sciences research.
• Job competition will remain keen because employment in this occupation is relatively small and few new jobs are expected.
• 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.
• In addition, mathematicians with experience in computer programming will better their job prospects in many 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 tenure-track positions—many graduates will need to find employment in industry and government.

Other occupations that require extensive knowledge of mathematics or, in some cases, a degree in mathematics include Actuaries, Computer networks, systems and database administrators, Computer Scientists, Computer software engineers and computer programmers, Computer System Analyst, Operation research analysts and Statisticians.

A strong background in mathematics also facilitates employment for Economists, Engineers, Financial Analysts, Market and survey researcher, Personal financial advisors, Physicists and astronomers, Teachers.