Career profile
Also known as AgentBased Modeler, Computational Scientist, Cryptographer, Cryptographic Vulnerability Analyst, Image Scientist, Lead Simulation Modeling Engineer
Mathematician
Also known as AgentBased 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.
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 computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.

Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
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.

Working with Computers


Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.

Getting Information


Observing, receiving, and otherwise obtaining information from all relevant sources.

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.
Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
Observing, receiving, and otherwise obtaining information from all relevant sources.
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 selfexpression 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
Independence.
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
Independence.
Occupations that satisfy this work value allow employees to work on their own and make decisions.
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 workrelated 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 workrelated problems.

Job requires analyzing information and using logic to address workrelated issues and problems.
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 workrelated 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 onthejob training, but most candidates will already have the required skills, knowledge, workrelated 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 subatomic structures and processes.

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.
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 subatomic 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
inductive 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.

Inductive Reasoning


The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).

Deductive Reasoning


The ability to apply general rules to specific problems to produce answers that make sense.

Information Ordering


The ability to arrange things or actions in a certain order or pattern according to a specific rule or set of rules (e.g., patterns of numbers, letters, words, pictures, mathematical operations).

The ability to choose the right mathematical methods or formulas to solve a problem.
The ability to add, subtract, multiply, or divide quickly and correctly.
The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).
The ability to apply general rules to specific problems to produce answers that make sense.
The ability to arrange things or actions in a certain order or pattern according to a specific rule or set of rules (e.g., patterns of numbers, letters, words, pictures, mathematical operations).
Critical Skills needed by Mathematicians
Skills
are developed capacities that enable people to function effectively in realworld 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 workrelated documents.

Active Learning


Understanding the implications of new information for both current and future problemsolving and decisionmaking.

Using mathematics to solve problems.
Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions, or approaches to problems.
Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.
Understanding written sentences and paragraphs in workrelated documents.
Understanding the implications of new information for both current and future problemsolving and decisionmaking.
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.