Mathematicians
15-2021.00

Conduct research in fundamental mathematics or in application of mathematical techniques to science, management, and other fields. Solve problems in various fields using mathematical methods.

Sample of reported job titles: Computational Mathematician, Computational Scientist, Cryptographer, Cryptographic Vulnerability Analyst, Image Scientist, Knowledge Engineer, Mathematician, Research Computing Specialist, Research Scientist, Researcher

Occupation-Specific Information

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.
  • Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.

back to top

Technology Skills

Hot technology
Hot Technologies are requirements most frequently included across all employer job postings.
In demand
In Demand skills are frequently included in employer job postings for this occupation.

back to top

Occupational Requirements

Work 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.
  • Updating and Using Relevant Knowledge — Keeping up-to-date technically and applying new knowledge to your job.
  • Working with Computers — Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
  • Interpreting the Meaning of Information for Others — Translating or explaining what information means and how it can be used.
  • Communicating with Supervisors, Peers, or Subordinates — Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person.
  • Training and Teaching Others — Identifying the educational needs of others, developing formal educational or training programs or classes, and teaching or instructing others.
  • Communicating with People Outside the Organization — Communicating with people outside the organization, representing the organization to customers, the public, government, and other external sources. This information can be exchanged in person, in writing, or by telephone or e-mail.
  • Identifying Objects, Actions, and Events — Identifying information by categorizing, estimating, recognizing differences or similarities, and detecting changes in circumstances or events.
  • Developing Objectives and Strategies — Establishing long-range objectives and specifying the strategies and actions to achieve them.
  • Providing Consultation and Advice to Others — Providing guidance and expert advice to management or other groups on technical, systems-, or process-related topics.
  • Establishing and Maintaining Interpersonal Relationships — Developing constructive and cooperative working relationships with others, and maintaining them over time.
  • Coaching and Developing Others — Identifying the developmental needs of others and coaching, mentoring, or otherwise helping others to improve their knowledge or skills.
  • Documenting/Recording Information — Entering, transcribing, recording, storing, or maintaining information in written or electronic/magnetic form.
  • Estimating the Quantifiable Characteristics of Products, Events, or Information — Estimating sizes, distances, and quantities; or determining time, costs, resources, or materials needed to perform a work activity.
  • Organizing, Planning, and Prioritizing Work — Developing specific goals and plans to prioritize, organize, and accomplish your work.

back to top

Detailed Work Activities

back to top

Work Context

back to top

Experience Requirements

Job Zone

Title
Job Zone Five: Extensive Preparation Needed
Education
Most of these occupations require graduate school. For example, they may require a master's degree, and some require a Ph.D., M.D., or J.D. (law degree).
Related Experience
Extensive skill, knowledge, and experience are needed for these occupations. Many require more than five years of experience. For example, surgeons must complete four years of college and an additional five to seven years of specialized medical training to be able to do their job.
Job Training
Employees may need some on-the-job training, but most of these occupations assume that the person will already have the required skills, knowledge, work-related experience, and/or training.
Job Zone Examples
These occupations often involve coordinating, training, supervising, or managing the activities of others to accomplish goals. Very advanced communication and organizational skills are required. Examples include pharmacists, lawyers, astronomers, biologists, clergy, physician assistants, and veterinarians.
SVP Range
Over 4 years of preparation (8.0 and above)

back to top

Training & Credentials

State training
Local training
Certifications
Apprenticeships
Have a career path or location in mind? Visit Apprenticeship.gov external site to find apprenticeship opportunities near you.

back to top

Worker Requirements

Skills

  • 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.
  • Active Learning — Understanding the implications of new information for both current and future problem-solving and decision-making.
  • Reading Comprehension — Understanding written sentences and paragraphs in work-related documents.
  • Science — Using scientific rules and methods to solve problems.
  • Judgment and Decision Making — Considering the relative costs and benefits of potential actions to choose the most appropriate one.
  • Writing — Communicating effectively in writing as appropriate for the needs of the audience.
  • Active Listening — Giving full attention to what other people are saying, taking time to understand the points being made, asking questions as appropriate, and not interrupting at inappropriate times.
  • Learning Strategies — Selecting and using training/instructional methods and procedures appropriate for the situation when learning or teaching new things.
  • Speaking — Talking to others to convey information effectively.
  • Systems Analysis — Determining how a system should work and how changes in conditions, operations, and the environment will affect outcomes.
  • Instructing — Teaching others how to do something.
  • Systems Evaluation — Identifying measures or indicators of system performance and the actions needed to improve or correct performance, relative to the goals of the system.
  • Monitoring — Monitoring/Assessing performance of yourself, other individuals, or organizations to make improvements or take corrective action.

back to top

Knowledge

  • Mathematics — Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
  • English Language — Knowledge of the structure and content of the English language including the meaning and spelling of words, rules of composition, and grammar.
  • 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.

back to top

Education

How much education does a new hire need to perform a job in this occupation? Respondents said:

  • 50%
     
    responded: Doctoral degree requiredmore info
  • 25%
     
    responded: Master’s degree requiredmore info
  • 8%
     
    responded: Bachelor’s degree required

back to top

Worker Characteristics

Abilities

  • 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).
  • 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).
  • Oral Comprehension — The ability to listen to and understand information and ideas presented through spoken words and sentences.
  • Written Comprehension — The ability to read and understand information and ideas presented in writing.
  • Oral Expression — The ability to communicate information and ideas in speaking so others will understand.
  • Category Flexibility — The ability to generate or use different sets of rules for combining or grouping things in different ways.
  • Fluency of Ideas — The ability to come up with a number of ideas about a topic (the number of ideas is important, not their quality, correctness, or creativity).
  • Problem Sensitivity — The ability to tell when something is wrong or is likely to go wrong. It does not involve solving the problem, only recognizing that there is a problem.
  • Written Expression — The ability to communicate information and ideas in writing so others will understand.
  • Near Vision — The ability to see details at close range (within a few feet of the observer).
  • Originality — The ability to come up with unusual or clever ideas about a given topic or situation, or to develop creative ways to solve a problem.
  • Flexibility of Closure — The ability to identify or detect a known pattern (a figure, object, word, or sound) that is hidden in other distracting material.
  • Perceptual Speed — The ability to quickly and accurately compare similarities and differences among sets of letters, numbers, objects, pictures, or patterns. The things to be compared may be presented at the same time or one after the other. This ability also includes comparing a presented object with a remembered object.
  • Selective Attention — The ability to concentrate on a task over a period of time without being distracted.
  • Speech Clarity — The ability to speak clearly so others can understand you.
  • Speech Recognition — The ability to identify and understand the speech of another person.
  • Speed of Closure — The ability to quickly make sense of, combine, and organize information into meaningful patterns.

back to top

Interests

Interest code: ICA
Want to discover your interests? Take the O*NET Interest Profiler at My Next Move.
  • Investigative — 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.
  • Conventional — 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.
  • Artistic — 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.

back to top

Work Values

  • Achievement — Occupations that satisfy this work value are results oriented and allow employees to use their strongest abilities, giving them a feeling of accomplishment. Corresponding needs are Ability Utilization and Achievement.
  • Recognition — Occupations that satisfy this work value offer advancement, potential for leadership, and are often considered prestigious. Corresponding needs are Advancement, Authority, Recognition and Social Status.
  • Independence — Occupations that satisfy this work value allow employees to work on their own and make decisions. Corresponding needs are Creativity, Responsibility and Autonomy.

back to top

Work Styles

  • 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.
  • Initiative — Job requires a willingness to take on responsibilities and challenges.
  • Independence — Job requires developing one's own ways of doing things, guiding oneself with little or no supervision, and depending on oneself to get things done.
  • Integrity — Job requires being honest and ethical.
  • Dependability — Job requires being reliable, responsible, and dependable, and fulfilling obligations.
  • Cooperation — Job requires being pleasant with others on the job and displaying a good-natured, cooperative attitude.
  • Adaptability/Flexibility — Job requires being open to change (positive or negative) and to considerable variety in the workplace.
  • Self-Control — Job requires maintaining composure, keeping emotions in check, controlling anger, and avoiding aggressive behavior, even in very difficult situations.
  • Leadership — Job requires a willingness to lead, take charge, and offer opinions and direction.
  • Stress Tolerance — Job requires accepting criticism and dealing calmly and effectively with high-stress situations.

back to top

Workforce Characteristics

Wages & Employment Trends

Median wages (2021)
$51.97 hourly, $108,100 annual
State wages
Local wages
Employment (2021)
2,000 employees
Projected growth (2021-2031)
Little or no change
Projected job openings (2021-2031)
100
State trends
Top industries (2021)

Source: Bureau of Labor Statistics 2021 wage data external site and 2021-2031 employment projections external site. “Projected growth” represents the estimated change in total employment over the projections period (2021-2031). “Projected job openings” represent openings due to growth and replacement.

back to top

Job Openings on the Web

State job openings
Local job openings

back to top

More Information

Related Occupations

back to top

back to top