Mathematicians use high-level mathematics and technology to develop new mathematical principles, understand relationships between existing principles, and solve real-world problems.

Mathematicians typically do the following:

- Expand mathematical knowledge by developing new principles
- Recognize previously unknown relationships between known mathematical principles
- Create models to resolve practical problems in fields such as business, government, engineering, and the sciences
- Develop computational methods and computer codes
- Compare inferences derived from models with observations or experiments.

Mathematicians work in the government and in private science and engineering research. They work on teams with engineers, scientists, and other professionals.

Workers other than formal mathematicians use mathematical techniques. For example, engineers, computer scientists, physicists, and economists use mathematics extensively. Some workers, such as statisticians, actuaries, and operations research analysts, are specialists in a particular branch of mathematics. Some people with a mathematics background become math teachers

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Students who are interested in mathematics should take as many math courses as possible in high school. For jobs as a mathematician with the federal government, candidates need at least a bachelor's degree with a major in mathematics or significant coursework in mathematics. Also, holders of bachelor's degrees who meet specific certification requirements may become middle or high school mathematics teachers.

Most colleges and universities offer a bachelor's degree in mathematics. Courses usually include calculus, differential equations, and linear and abstract algebra. Many colleges and universities advise or require mathematics students to take courses in a related field, such as computer science, engineering, or physical science.

Candidates who have a double major in mathematics and a related discipline are particularly desirable to many employers. In private industry, mathematicians typically need an advanced degree, either a master's degree or a doctorate. Many universities offer master's and doctoral degrees in theoretical or applied mathematics.

A master’s degree generally takes two years beyond the bachelor's degree. That is often enough for many positions in applied mathematics. However, most people with a master's degree in mathematics do not work as mathematicians. Instead, they work in related fields, including computer science, where they have titles such as computer programmer, systems analyst, and systems engineer, and statistics, where they are called statisticians.

For a position as a professor of mathematics in a college or university, a doctorate is usually required. A doctoral degree usually takes at least five years of study beyond the bachelor's degree.

Mathematicians work in the government and in private science and engineering research companies. They often work with engineers, scientists, and other professionals and therefore must often work around others' schedules.

Mathematicians who work in postsecondary education usually have a mix of teaching and research responsibilities. Many academic mathematicians do research by themselves or in collaboration with other mathematicians. Collaborators work together at the same institution or from different locations, communicating electronically. Mathematicians in academia often have help from graduate students.