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Career profile Mathematician

Also known as Agent-Based Modeler, Computational Scientist, Cryptographer, Cryptographic Vulnerability Analyst, Image Scientist, Lead Simulation Modeling Engineer


Also known as Agent-Based Modeler, Computational Scientist, Cryptographer

Interests Profile
  • Investigative
  • Conventional
  • Artistic
Pay Range
$61,130 - $170,150 (annual)
Required Skills
  • Mathematics
  • Critical Thinking
  • Complex Problem Solving
Knowledge Areas
  • Mathematics
  • Computers and Electronics
  • Education and Training
Core tasks
  • Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
  • Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
  • Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
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What does a Mathematician do?

Mathematicians conduct research in fundamental mathematics or in application of mathematical techniques to science, management, and other fields.

In addition, Mathematicians solve problems in various fields using mathematical methods.

What kind of tasks does a Mathematician perform regularly?

Mathematicians are often responsible for overseeing or executing some or all of the following tasks:

  • Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
  • Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
  • Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
  • Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
  • Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
  • Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
  • Perform computations and apply methods of numerical analysis to data.
  • Assemble sets of assumptions and explore the consequences of each set.
  • Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
  • Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.

The above responsibilities are specific to Mathematicians. More generally, Mathematicians are involved in several broader types of activities:

Analyzing Data or Information
Identifying the underlying principles, reasons, or facts of information by breaking down information or data into separate parts.
Making Decisions and Solving Problems
Analyzing information and evaluating results to choose the best solution and solve problems.
Processing Information
Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
Getting Information
Observing, receiving, and otherwise obtaining information from all relevant sources.
Thinking Creatively
Developing, designing, or creating new applications, ideas, relationships, systems, or products, including artistic contributions.

What is a Mathematician salary?

The median salary for a Mathematician is $110,860, and the average salary is $112,530. Both the median and average roughly describe the middle of the Mathematician salary range, but the average is more easily affected by extremely high or low salaries.

Many Mathematicians earn significantly more or less than the average, due to several factors. About 10% of Mathematicians earn less than $61,130 per year, 25% earn less than $79,280, 75% earn less than $134,680, and 90% earn less than $170,150.

Between the years of 2020 and 2030, the number of Mathematicians is expected to change by 3.7%, and there should be roughly 200 open positions for Mathematicians every year.

Median annual salary
Typical salary range
$61,130 - $170,150
Projected growth (2020 - 2030)

What personality traits are common among Mathematicians?


Career interests describe a person's preferences for different types of working environments and activities. When a person's interest match the demands of an occupation, people are usually more engaged and satisfied in that role.

Compared to most occupations, those who work as a Mathematician are usually higher in their Investigative, Conventional, and Artistic interests.

Mathematicians typically have very strong Investigative interests. Investigative occupations frequently involve working with ideas, and require an extensive amount of thinking. These occupations can involve searching for facts and figuring out problems mentally.

Also, Mathematicians typically have moderate Conventional interests. Conventional occupations frequently involve following set procedures and routines. These occupations can include working with data and details more than with ideas. Usually there is a clear line of authority to follow.

Lastly, Mathematicians typically have moderate Artistic interests. Artistic occupations frequently involve working with forms, designs and patterns. They often require self-expression and the work can be done without following a clear set of rules.


People differ in their values, or what is most important to them for building job satisfaction and fulfillment.

Compared to most people, those working as a Mathematician tend to value Achievement, Recognition, and Working Conditions.

Most importantly, Mathematicians very strongly value Achievement. Occupations that satisfy this work value are results oriented and allow employees to use their strongest abilities, giving them a feeling of accomplishment.

Second, Mathematicians strongly value Recognition. Occupations that satisfy this work value offer advancement, potential for leadership, and are often considered prestigious.

Lastly, Mathematicians strongly value Working Conditions. Occupations that satisfy this work value offer job security and good working conditions.

Psychological Demands

Each occupation brings its own set of psychological demands, which describe the characteristics necessary to perform the job well.

In order to perform their job successfully, people who work as Mathematicians must consistently demonstrate qualities such as analytical thinking, attention to detail, and persistence.

Below, you'll find a list of qualities typically required of Mathematicians, ranked by importance:

Analytical Thinking
Job requires analyzing information and using logic to address work-related issues and problems.
Attention to Detail
Job requires being careful about detail and thorough in completing work tasks.
Job requires persistence in the face of obstacles.
Job requires establishing and maintaining personally challenging achievement goals and exerting effort toward mastering tasks.
Job requires creativity and alternative thinking to develop new ideas for and answers to work-related problems.

What education and training do Mathematicians need?

Many Mathematicians have earned a graduate degree. For example, they may require a master's degree, and some require a doctoral degree, such as a Ph.D., M.D., or J.D..

Mathematicians may need some on-the-job training, but most candidates will already have the required skills, knowledge, work-related experience, and/or training.

Educational degrees among Mathematicians

  • 0.4% did not complete high school or secondary school
  • 2.8% completed high school or secondary school
  • 6.9% completed some college coursework
  • 3.8% earned a Associate's degree
  • 37.2% earned a Bachelor's degree
  • 35.4% earned a Master's degree
  • 13.5% earned a doctorate or professional degree

Knowledge and expertise required by Mathematicians

Mathematicians may benefit from understanding of specialized subject areas, such as mathematics, computers and electronics, or education and training knowledge.

The list below shows several areas in which most Mathematicians might want to build proficiency, ranked by importance.

Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
Computers and Electronics
Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.
Education and Training
Knowledge of principles and methods for curriculum and training design, teaching and instruction for individuals and groups, and the measurement of training effects.
Engineering and Technology
Knowledge of the practical application of engineering science and technology. This includes applying principles, techniques, procedures, and equipment to the design and production of various goods and services.
Knowledge and prediction of physical principles, laws, their interrelationships, and applications to understanding fluid, material, and atmospheric dynamics, and mechanical, electrical, atomic and sub-atomic structures and processes.

Important Abilities needed by Mathematicians

Mathematicians must develop a particular set of abilities to perform their job well. Abilities are individual capacities that influence a person's information processing, sensory perception, motor coordination, and physical strength or endurance. Individuals may naturally have certain abilities without explicit training, but most abilities can be sharpened somewhat through practice.

For example, Mathematicians need abilities such as mathematical reasoning, number facility, and deductive reasoning in order to perform their job at a high level. The list below shows several important abilities for Mathematicians, ranked by their relative importance.

Mathematical Reasoning
The ability to choose the right mathematical methods or formulas to solve a problem.
Number Facility
The ability to add, subtract, multiply, or divide quickly and correctly.
Deductive Reasoning
The ability to apply general rules to specific problems to produce answers that make sense.
Inductive Reasoning
The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).
Oral Comprehension
The ability to listen to and understand information and ideas presented through spoken words and sentences.

Critical Skills needed by Mathematicians

Skills are developed capacities that enable people to function effectively in real-world settings. Unlike abilities, skills are typically easier to build through practice and experience. Skills influence effectiveness in areas such as learning, working with others, design, troubleshooting, and more.

Mathematicians frequently use skills like mathematics, critical thinking, and complex problem solving to perform their job effectively. The list below shows several critical skills for Mathematicians, ranked by their relative importance.

Using mathematics to solve problems.
Critical Thinking
Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions, or approaches to problems.
Complex Problem Solving
Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
Reading Comprehension
Understanding written sentences and paragraphs in work-related documents.
Active Learning
Understanding the implications of new information for both current and future problem-solving and decision-making.

What is the source of this information?

The information provided on this page is adapted from data and descriptions published by the U.S. Department of Labor, Employment and Training Administration under the CC BY 4.0 license. TraitLab has modified some information for ease of use and reading, and the U.S. Department of Labor, Employment, and Training Administration has not approved, endorsed, or tested these modifications.

If you have any questions or suggestions about this information, please send a message.