Mathematicians use advanced mathematics to develop and understand mathematical principles, analyze data, and solve real-world problems.


Mathematicians typically do the following:

  • Expand knowledge in mathematical areas, such as algebra or geometry, by developing new rules, theories, and concepts
  • Use mathematical formulas and models to prove or disprove theories
  • Apply mathematical theories and techniques to solve practical problems in business, engineering, the sciences, or other fields
  • Develop mathematical or statistical models to analyze data
  • Interpret data and report conclusions from their analyses
  • Use data analysis to support and improve business decisions
  • Read professional journals, talk with other mathematicians, and attend professional conferences to maintain knowledge of current trends

The following are examples of types of mathematicians:

Applied mathematicians use theories and techniques, such as mathematical modeling, to solve practical problems. These mathematicians typically work with individuals in other occupations to solve these problems. For example, they may work with chemists and materials scientists and chemical engineers to analyze the effectiveness of new drugs. Other applied mathematicians may work with industrial designers to study the aerodynamic characteristics of new automobiles.

Theoretical mathematicians do research to identify unexplained issues in mathematics and resolve them. They are primarily concerned with exploring new areas and relationships of mathematical theories to increase knowledge and understanding about the field. Although some may not consider the practical use of their findings, the knowledge they develop can be an important part of many scientific and engineering achievements.

Despite the differences, these areas of mathematics frequently overlap. Many mathematicians will use both applied and theoretical knowledge in their job duties.

However, most people with a degree in mathematics or who develop mathematical theories and models are not formally known as mathematicians. Instead, they work in related fields and professions. In the computer systems design and related services industries, they may be known as computer programmers or systems analysts. In finance, they may be known as quantitative analysts, financial analysts, or statisticians.

Computer and information research scientists, physicists and astronomers, economists, actuaries, operations research analysts, and many other occupations also use mathematics extensively.

Some people with a mathematics background become middle school or high school math teachers.

Many people with a Ph.D. in mathematics, particularly theoretical mathematics, work as postsecondary teachers in education institutions. They usually have a mix of teaching and research responsibilities. Some may do individual research or collaborate with other professors or mathematicians. Collaborators may work together at the same institution or from different locations.

Work Environment

Mathematicians held about 3,500 jobs in 2012. Most mathematicians work for the federal government or for private scientific and engineering research and development companies.

The industries that employed the most mathematicians in 2012 were as follows:

Federal government 30%
Scientific research and development services 20
Educational services; state, local, and private 18
Management of companies and enterprises 7
Manufacturing 3

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

Work Schedules

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

Education and Training

Mathematicians typically need a master’s degree in mathematics. However, there are some positions available for those with a bachelor's degree.


In private industry, mathematicians typically need an advanced degree, either a master’s degree or a doctorate. For jobs with the federal government, candidates need at least a bachelor’s degree in mathematics or significant coursework in mathematics.

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, physics, or statistics. Candidates who have a double major in mathematics and a related discipline are particularly desirable to many employers.

Many universities offer master’s and doctoral degrees in theoretical or applied mathematics. Many students who get a doctoral degree work as professors of mathematics in a college or university, rather than work in government or private industry.

Also, holders of bachelor’s degrees who meet state certification requirements may become middle or high school mathematics teachers.

Students who are interested in becoming mathematicians should take as many math courses as possible in high school.

Important Qualities

Analytical skills. Mathematicians use mathematical techniques and models to analyze large amounts of data. They must be precise and accurate in their analysis.

Communication skills. Mathematicians must interact with and propose solutions to people who may not have extensive knowledge of mathematics.

Math skills. Mathematicians use statistics, calculus, and linear algebra to develop their models and analyses.

Problem-solving skills. Mathematicians must devise new solutions to problems encountered by scientists or engineers.


The median annual wage for mathematicians was $101,360 in May 2012. 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 $56,040, and the top 10 percent earned more than $152,950.

In May 2012, the median annual wages for mathematicians in the top five industries in which these mathematicians worked were as follows:

Scientific research and development services $118,030
Manufacturing 116,860
Federal government 106,360
Management of companies and enterprises 74,980
Educational services; state, local, and private 66,590

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

Job Outlook

Employment of mathematicians is projected to grow 23 percent from 2012 to 2022, much faster than the average for all occupations. However, because it is a small occupation, the fast growth will result in only about 800 new jobs over the 10-year period.

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 mathematicians to analyze the large amount of information and data collected. Analyses will help companies improve their business processes, design and develop new products, and even advertise products to potential customers.

Mathematicians will also be needed to help information security analysts create data-security systems to protect the confidentiality and personal information of individuals.

Job Prospects

Because the occupation is small and there are relatively few mathematician positions, strong competition for jobs is expected. Despite the strong competition for mathematician positions, many candidates with a background in advanced mathematical techniques and modeling will find positions in other closely related fields.

Those with a graduate degree in math, very strong quantitative and data analysis skills, and a background in a related discipline, such as business, computer science, or statistics, should have the best job prospects. Computer programming skills are also important to many employers.

For More Information

For more information about mathematicians, including training, especially for doctoral-level employment, visit

American Mathematical Society

For specific information on careers in applied mathematics, visit

Society for Industrial and Applied Mathematics

For information on job openings as a mathematician with the federal government, visit

Office of Personnel Management