Mathematicians
15-2021.00
Updated 2025

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: Agent-Based Modeler, Computational Mathematician, Computational Scientist, Cryptographer, Cryptographic Vulnerability Analyst, Mathematician, Research Computing Specialist, Research Scientist, Researcher

Occupation-Specific Information

Tasks

  • Mentor others on mathematical techniques.
  • Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
  • Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
  • Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
  • Assemble sets of assumptions, and explore the consequences of each set.
  • Perform computations and apply methods of numerical analysis to data.
  • Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
  • 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.
  • Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
  • 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.
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Technology Skills

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Occupational Requirements

Work Activities

  • 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.
  • Updating and Using Relevant Knowledge — Keeping up-to-date technically and applying new knowledge to your job.
  • Processing Information — Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying information or data.
  • Training and Teaching Others — Identifying the educational needs of others, developing formal educational or training programs or classes, and teaching or instructing others.
  • Working with Computers — Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
  • Making Decisions and Solving Problems — Analyzing information and evaluating results to choose the best solution and solve problems.
  • Getting Information — Observing, receiving, and otherwise obtaining information from all relevant sources.
  • 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.
  • Coaching and Developing Others — Identifying the developmental needs of others and coaching, mentoring, or otherwise helping others to improve their knowledge or skills.
  • Organizing, Planning, and Prioritizing Work — Developing specific goals and plans to prioritize, organize, and accomplish your work.
  • Documenting/Recording Information — Entering, transcribing, recording, storing, or maintaining information in written or electronic/magnetic form.
  • Developing Objectives and Strategies — Establishing long-range objectives and specifying the strategies and actions to achieve them.
  • 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.
  • 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.
  • Providing Consultation and Advice to Others — Providing guidance and expert advice to management or other groups on technical, systems-, or process-related topics.

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Work Context

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
(8.0 and above)

Training & Credentials

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Certifications
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Apprenticeship Opportunities

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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.
  • Active Learning — Understanding the implications of new information for both current and future problem-solving and decision-making.
  • 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.
  • Judgment and Decision Making — Considering the relative costs and benefits of potential actions to choose the most appropriate one.
  • Science — Using scientific rules and methods to solve problems.
  • 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.
  • Instructing — Teaching others how to do something.
  • Monitoring — Monitoring/Assessing performance of yourself, other individuals, or organizations to make improvements or take corrective action.
  • Systems Analysis — Determining how a system should work and how changes in conditions, operations, and the environment will affect outcomes.
  • 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.

Knowledge

  • Mathematics — Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
  • 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.
  • Computers and Electronics — Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.
  • English Language — Knowledge of the structure and content of the English language including the meaning and spelling of words, and rules of composition and grammar.
  • 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.

Education

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

  • 45%
     
    Doctoral degree required
  • 25%
     
    Master’s degree required
  • 10%
     
    Bachelor’s degree required

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.
  • Oral Comprehension — The ability to listen to and understand information and ideas presented through spoken words and sentences.
  • Oral Expression — The ability to communicate information and ideas in speaking so others will understand.
  • Written Comprehension — The ability to read and understand information and ideas presented in writing.
  • Written Expression — The ability to communicate information and ideas in writing so others will understand.
  • Deductive Reasoning — The ability to apply general rules to specific problems to produce answers that make sense.
  • Category Flexibility — The ability to generate or use different sets of rules for combining or grouping things in different ways.
  • 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).
  • 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).
  • 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.
  • 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.
  • Near Vision — The ability to see details at close range (within a few feet of the observer).
  • 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.
  • 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.

Interests

Interest code: IC
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  • Investigative — Work involves studying and researching non-living objects, living organisms, disease or other forms of impairment, or human behavior. Investigative occupations are often associated with physical, life, medical, or social sciences, and can be found in the fields of humanities, mathematics/statistics, information technology, or health care service.
  • Conventional — Work involves following procedures and regulations to organize information or data, typically in a business setting. Conventional occupations are often associated with office work, accounting, mathematics/statistics, information technology, finance, or human resources.

Work Styles

  • Innovation — A tendency to be inventive, to be imaginative, and to adopt new perspectives on ways to accomplish work.
  • Perseverance — A tendency to exhibit determination and resolve to perform or complete tasks in the face of difficult circumstances or obstacles at work.
  • Achievement Orientation — A tendency to establish and maintain personally challenging work-related goals, set high work-related standards, and exert high effort toward meeting those goals and standards.
  • Intellectual Curiosity — A tendency to seek out and acquire new work-related knowledge and obtain a deep understanding of work-related subjects.
  • Attention to Detail — A tendency to be detail-oriented, organized, and thorough in completing work.

Workforce Characteristics

Wages & Employment Trends

Median wages (2024)
$58.50 hourly, $121,680 annual
State wages
Local wages
Employment (2024)
2,400 employees
Projected growth (2024-2034)
Decline (-1% or lower)
Projected job openings (2024-2034)
100
State trends
Top industries (2024)

Source: Bureau of Labor Statistics 2024 wage data and 2024-2034 employment projections . “Projected growth” represents the estimated change in total employment over the projections period (2024-2034). “Projected job openings” represent openings due to growth and replacement.

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