Mathematicians
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.
Also Known As:
Agent-Based Modeler
Computational Mathematician
Computational Scientist
Cryptographer
Cryptographic Vulnerability Analyst
Mathematician
Research Computing Specialist
Research Scientist
Researcher
Wages
Annual wages for Mathematicians in United States
Job Outlook
Below Average
New job opportunities are less likely in the future
United States
2034 Projected Employment
2,400
-1% Change From 2024
Explore Mathematicians video
Tasks you might complete in a day.
- Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
- Assemble sets of assumptions, and explore the consequences of each set.
- Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
- 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.
- Mentor others on mathematical techniques.
- Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
- Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
- Perform computations and apply methods of numerical analysis to data.
- Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
- 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.
- Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
- Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
- Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
- Mentor others on mathematical techniques.
Subject areas you may need to master.
- Customer and Personal Service - Knowledge of principles and processes for providing customer and personal services. This includes customer needs assessment, meeting quality standards for services, and evaluation of customer satisfaction.
- Mechanical - Knowledge of machines and tools, including their designs, uses, repair, and maintenance.
- Philosophy and Theology - Knowledge of different philosophical systems and religions. This includes their basic principles, values, ethics, ways of thinking, customs, practices, and their impact on human culture.
- 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.
- Foreign Language - Knowledge of the structure and content of a foreign (non-English) language including the meaning and spelling of words, rules of composition and grammar, and pronunciation.
- Sales and Marketing - Knowledge of principles and methods for showing, promoting, and selling products or services. This includes marketing strategy and tactics, product demonstration, sales techniques, and sales control systems.
- 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.
- Chemistry - Knowledge of the chemical composition, structure, and properties of substances and of the chemical processes and transformations that they undergo. This includes uses of chemicals and their interactions, danger signs, production techniques, and disposal methods.
- Medicine and Dentistry - Knowledge of the information and techniques needed to diagnose and treat human injuries, diseases, and deformities. This includes symptoms, treatment alternatives, drug properties and interactions, and preventive health-care measures.
- Public Safety and Security - Knowledge of relevant equipment, policies, procedures, and strategies to promote effective local, state, or national security operations for the protection of people, data, property, and institutions.
- Design - Knowledge of design techniques, tools, and principles involved in production of precision technical plans, blueprints, drawings, and models.
- Sociology and Anthropology - Knowledge of group behavior and dynamics, societal trends and influences, human migrations, ethnicity, cultures, and their history and origins.
- Administrative - Knowledge of administrative and office procedures and systems such as word processing, managing files and records, stenography and transcription, designing forms, and workplace terminology.
- Mathematics - Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their applications.
- Personnel and Human Resources - Knowledge of principles and procedures for personnel recruitment, selection, training, compensation and benefits, labor relations and negotiation, and personnel information systems.
- Fine Arts - Knowledge of the theory and techniques required to compose, produce, and perform works of music, dance, visual arts, drama, and sculpture.
- History and Archeology - Knowledge of historical events and their causes, indicators, and effects on civilizations and cultures.
- Therapy and Counseling - Knowledge of principles, methods, and procedures for diagnosis, treatment, and rehabilitation of physical and mental dysfunctions, and for career counseling and guidance.
- Food Production - Knowledge of techniques and equipment for planting, growing, and harvesting food products (both plant and animal) for consumption, including storage/handling techniques.
- Economics and Accounting - Knowledge of economic and accounting principles and practices, the financial markets, banking, and the analysis and reporting of financial data.
- Communications and Media - Knowledge of media production, communication, and dissemination techniques and methods. This includes alternative ways to inform and entertain via written, oral, and visual media.
- 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.
- Telecommunications - Knowledge of transmission, broadcasting, switching, control, and operation of telecommunications systems.
- Administration and Management - Knowledge of business and management principles involved in strategic planning, resource allocation, human resources modeling, leadership technique, production methods, and coordination of people and resources.
- Production and Processing - Knowledge of raw materials, production processes, quality control, costs, and other techniques for maximizing the effective manufacture and distribution of goods.
- Computers and Electronics - Knowledge of circuit boards, processors, chips, electronic equipment, and computer hardware and software, including applications and programming.
- 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.
- Building and Construction - Knowledge of materials, methods, and the tools involved in the construction or repair of houses, buildings, or other structures such as highways and roads.
- Geography - Knowledge of principles and methods for describing the features of land, sea, and air masses, including their physical characteristics, locations, interrelationships, and distribution of plant, animal, and human life.
- Psychology - Knowledge of human behavior and performance; individual differences in ability, personality, and interests; learning and motivation; psychological research methods; and the assessment and treatment of behavioral and affective disorders.
- Biology - Knowledge of plant and animal organisms, their tissues, cells, functions, interdependencies, and interactions with each other and the environment.
- Transportation - Knowledge of principles and methods for moving people or goods by air, rail, sea, or road, including the relative costs and benefits.
- Law and Government - Knowledge of laws, legal codes, court procedures, precedents, government regulations, executive orders, agency rules, and the democratic political process.
Strengths you may need in this role.
- Science - Using scientific rules and strategies to solve problems.
- Equipment Selection - Deciding what kind of tools and equipment are needed to do a job.
- Complex Problem Solving - Noticing a problem and figuring out the best way to solve it.
- Operation and Control - Using equipment or systems.
- Active Listening - Listening to others, not interrupting, and asking good questions.
- Service Orientation - Looking for ways to help people.
- Reading Comprehension - Reading work-related information.
- Speaking - Talking to others.
- Critical Thinking - Thinking about the pros and cons of different ways to solve a problem.
- Instructing - Teaching people how to do something.
- Judgment and Decision Making - Thinking about the pros and cons of different options and picking the best one.
- Management of Material Resources - Managing equipment and materials.
- Quality Control Analysis - Testing how well a product or service works.
- Equipment Maintenance - Planning and doing the basic maintenance on equipment.
- Time Management - Managing your time and the time of other people.
- Systems Analysis - Figuring out how a system should work and how changes in the future will affect it.
- Mathematics - Using math to solve problems.
- Coordination - Changing what is done based on other people's actions.
- Technology Design - Making equipment and technology useful for customers.
- Persuasion - Talking people into changing their minds or their behavior.
- Writing - Writing things for co-workers or customers.
- Monitoring - Keeping track of how well people and/or groups are doing in order to make improvements.
- Learning Strategies - Using the best training or teaching strategies for learning new things.
- Social Perceptiveness - Understanding people's reactions.
- Operations Analysis - Figuring out what a product or service needs to be able to do.
- Negotiation - Bringing people together to solve differences.
- Installation - Installing equipment, machines, wiring, or computer programs.
- Active Learning - Figuring out how to use new ideas or things.
- Programming - Writing computer programs.
- Operations Monitoring - Watching gauges, dials, or display screens to make sure a machine is working.
- Troubleshooting - Figuring out what is causing equipment, machines, wiring, or computer programs to not work.
- Management of Financial Resources - Making spending decisions and keeping track of what is spent.
- Repairing - Repairing machines or systems using the right tools.
- Management of Personnel Resources - Selecting and managing the best workers for a job.
- Systems Evaluation - Measuring how well a system is working and how to improve it.
- Static Strength - Lifting, pushing, pulling, or carrying.
- Extent Flexibility - Bending, stretching, twisting, or reaching with your body, arms, and/or legs.
- Night Vision - Seeing at night or under low light.
- Originality - Creating new and original ideas.
- Explosive Strength - Jumping, sprinting, or throwing something.
- Glare Sensitivity - Seeing something even if there is a glare or very bright light.
- Oral Comprehension - Listening and understanding what people say.
- Spatial Orientation - Knowing where things are around you.
- Visualization - Imagining how something will look after it is moved around or changed.
- Manual Dexterity - Holding or moving items with your hands.
- Written Expression - Communicating by writing.
- Written Comprehension - Reading and understanding what is written.
- Near Vision - Seeing details up close.
- Deductive Reasoning - Using rules to solve problems.
- Information Ordering - Ordering or arranging things.
- Fluency of Ideas - Coming up with lots of ideas.
- Depth Perception - Deciding which thing is closer or farther away from you, or deciding how far away it is from you.
- Far Vision - Seeing details that are far away.
- Auditory Attention - Paying attention to one sound while there are other distracting sounds.
- Memorization - Remembering words, numbers, pictures, or steps.
- Multilimb Coordination - Using your arms and/or legs together while sitting, standing, or lying down.
- Speed of Limb Movement - Quickly moving your arms and legs.
- Flexibility of Closure - Seeing hidden patterns.
- Wrist-Finger Speed - Making fast, simple, repeated movements of your fingers, hands, and wrists.
- Selective Attention - Paying attention to something without being distracted.
- Category Flexibility - Grouping things in different ways.
- Inductive Reasoning - Making general rules or coming up with answers from lots of detailed information.
- Stamina - Exercising for a long time without getting out of breath.
- Dynamic Flexibility - Quickly and repeatedly bending, stretching, twisting, or reaching out with your body, arms, and/or legs.
- Perceptual Speed - Quickly comparing groups of letters, numbers, pictures, or other things.
- Finger Dexterity - Putting together small parts with your fingers.
- Visual Color Discrimination - Noticing the difference between colors, including shades and brightness.
- Sound Localization - Noticing the direction that a sound came from.
- Number Facility - Adding, subtracting, multiplying, or dividing.
- Peripheral Vision - Seeing something to your side when your are looking ahead.
- Speech Clarity - Speaking clearly.
- Speech Recognition - Recognizing spoken words.
- Gross Body Equilibrium - Keeping your balance or staying upright.
- Trunk Strength - Using your lower back and stomach.
- Time Sharing - Doing two or more things at the same time.
- Speed of Closure - Quickly knowing what you are looking at.
- Rate Control - Changing when and how fast you move based on how something else is moving.
- Reaction Time - Quickly moving your hand, finger, or foot based on a sound, light, picture or other command.
- Arm-Hand Steadiness - Keeping your arm or hand steady.
- Response Orientation - Quickly deciding if you should move your hand, foot, or other body part.
- Control Precision - Quickly changing the controls of a machine, car, truck or boat.
- Problem Sensitivity - Noticing when problems happen.
- Mathematical Reasoning - Choosing the right type of math to solve a problem.
- Dynamic Strength - Exercising for a long time without your muscles getting tired.
- Hearing Sensitivity - Telling the difference between sounds.
- Oral Expression - Communicating by speaking.
- Gross Body Coordination - Moving your arms, legs, and mid-section together while your whole body is moving.
Average Education Attained
Highest level of education earned by people in this career.
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Content sourced from United States Department of Labor Employment and Training Administration ("DOLETA") and the Minnesota Department of Employment & Economic Development ("DEED")