Career profile for Mathematician

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:

Activities	Importance	Details
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.

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: $110,860
Typical salary range: $61,130 - $170,150
Projected growth (2020 - 2030): 3.7%

What personality traits are common among Mathematicians?

Interests

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.

Values

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:

Demands	Importance	Details
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.
Persistence		Job requires persistence in the face of obstacles.
Achievement/Effort		Job requires establishing and maintaining personally challenging achievement goals and exerting effort toward mastering tasks.
Innovation		Job requires creativity and alternative thinking to develop new ideas for and answers to work-related problems.

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.

Persistence

Job requires persistence in the face of obstacles.

Achievement/Effort

Job requires establishing and maintaining personally challenging achievement goals and exerting effort toward mastering tasks.

Innovation

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 areas	Importance	Details
Mathematics		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.
Physics		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.

Mathematics

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.

Physics

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.

Abilities	Importance	Details
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.

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.

Skills	Importance	Details
Mathematics		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.

Mathematics

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.

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