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 systemsâ€”codesâ€”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.

## Work Environment

Mathematicians held about 2,700 jobs in 2020. The largest employers of mathematicians were as follows:

- Federal government - 47%
- Professional, scientific, and technical services - 26%
- Colleges, universities, and professional schools; state, local, and private - 17%

Statisticians held about 42,000 jobs in 2020. The largest employers of statisticians were as follows:

- Research and development in the physical, engineering, and life sciences - 14%
- Federal government - 12%
- Healthcare and social assistance - 9%
- Insurance carriers and related activities - 8%
- Colleges, universities, and professional schools; state, local, and private 7%

Mathematicians and statisticians typically work in offices. They also may work on teams with engineers, scientists, and other specialists.

### Work Schedules

Most mathematicians and statisticians work full time. Deadlines and last-minute requests for data or analysis may require overtime. In addition, these workers may travel to attend seminars and conferences.

## Education & Training Required

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 the Federal Government, entry-level job candidates usually must have at least a bachelor's degree with a major in mathematics or 24 semester hours of mathematics courses. Outside the Federal Government, 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.

Most colleges and universities offer a bachelor's degree in mathematics, and many universities offer master's and doctoral degrees in pure or applied mathematics. Courses usually required for these programs 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. In graduate programs, students also conduct research and take advanced courses, usually specializing in a subfield of mathematics.

Many colleges and universities advise or require students majoring in mathematics to take courses in a closely related field, 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.

## Other Skills Required

For jobs in applied mathematics, training in the field in which 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 to have good reasoning to identify, analyze, and apply basic principles to technical problems. Communication skills also are important, because mathematicians must be able to interact and discuss proposed solutions with people who may not have extensive knowledge of mathematics.

## How to Advance

The majority of those with a 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. In these occupations, workers can advance to management positions.

## Job Outlook

Overall employment of mathematicians and statisticians is projected to grow 33 percent from 2020 to 2030, much faster than the average for all occupations.

About 5,200 openings for mathematicians and statisticians are projected each year, on average, over the decade. Many of those openings are expected to result from the need to replace workers who transfer to different occupations or exit the labor force, such as to retire.

### Employment

Employment growth for statisticians is expected to result from more widespread use of statistical analysis to inform business, healthcare, and policy decisions. The amount of digitally stored data will increase over the next decade as more people and companies conduct business online and use social media, smartphones, and other mobile devices. As a result, businesses will increasingly need statisticians to analyze the large amount of information and data collected. Statistical analyses will help companies improve their business processes, design and develop new products, and advertise products to potential customers.

Many of the new jobs for statisticians are expected to be in research and development, consulting, and computer systems design and related services.

Much of the employment growth for mathematicians is expected to be in research-based roles in academia, research and development, and consulting services.

## Earnings

The median annual wage for mathematicians was $108,100 in May 2021. The median wage is the wage at which half the workers in an occupation earned more than that amount and half earned less. The lowest 10 percent earned less than $61,760, and the highest 10 percent earned more than $169,500.

The median annual wage for statisticians was $95,570 in May 2021. The lowest 10 percent earned less than $49,350, and the highest 10 percent earned more than $157,300.

In May 2021, the median annual wages for mathematicians in the top industries in which they worked were as follows:

- Professional, scientific, and technical services - $129,800
- Federal government - $115,610
- Colleges, universities, and professional schools; state, local, and private - $61,600

In May 2021, the median annual wages for statisticians in the top industries in which they worked were as follows:

- Research and development in the physical, engineering, and life sciences - $114,770
- Federal government - $114,050
- Insurance carriers and related activities - $83,820
- Healthcare and social assistance - $79,060
- Colleges, universities, and professional schools; state, local, and private - $77,750

Most mathematicians and statisticians work full time. Deadlines and last-minute requests for data or analysis may require overtime. In addition, these workers may travel to attend seminars and conferences.