[Core] [20% incumbents] Mentor others on mathematical techniques.
  DWAs: Collaborate on research activities with scientists or technical specialists. | Provide technical guidance to other personnel.

[Core] [20% incumbents] Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
  DWAs: Update knowledge about emerging industry or technology trends.

[Core] [20% incumbents] Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
  DWAs: Develop scientific or mathematical models.

[Core] [20% incumbents] Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
  DWAs: Present research results to others. | Prepare analytical reports.

[Core] [20% incumbents] Assemble sets of assumptions, and explore the consequences of each set.
  DWAs: Analyze data to identify trends or relationships among variables.

[Core] [20% incumbents] Perform computations and apply methods of numerical analysis to data.
  DWAs: Analyze data to identify trends or relationships among variables.

[Core] [20% incumbents] Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
  DWAs: Analyze data to identify trends or relationships among variables.

[Core] [20% incumbents] Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
  DWAs: Review professional literature to maintain professional knowledge. | Update professional knowledge.

[Core] [20% incumbents] Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
  DWAs: Design computer modeling or simulation programs.

[Core] [20% incumbents] Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
  DWAs: Apply mathematical principles or statistical approaches to solve problems in scientific or applied fields.

[Core] [20% incumbents] Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
  DWAs: Determine appropriate methods for data analysis.

[Supplemental] [20% incumbents] Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
  DWAs: Analyze security of systems, network, or data. | Develop computer or information security policies or procedures.

--- SKILLS ---
  Mathematics (imp:5.00 lvl:6.00) — Using mathematics to solve problems.
  Critical Thinking (imp:4.12 lvl:5.00) — Using logic and reasoning to identify the strengths and weaknesses of alternativ
  Reading Comprehension (imp:4.00 lvl:5.00) — Understanding written sentences and paragraphs in work-related documents.
  Active Learning (imp:4.00 lvl:5.12) — Understanding the implications of new information for both current and future pr
  Writing (imp:3.62 lvl:4.62) — Communicating effectively in writing as appropriate for the needs of the audienc
  Science (imp:3.62 lvl:4.50) — Using scientific rules and methods to solve problems.
  Active Listening (imp:3.38 lvl:4.00) — Giving full attention to what other people are saying, taking time to understand
  Speaking (imp:3.25 lvl:4.00) — Talking to others to convey information effectively.
  Learning Strategies (imp:3.25 lvl:3.88) — Selecting and using training/instructional methods and procedures appropriate fo
  Monitoring (imp:3.00 lvl:3.00) — Monitoring/Assessing performance of yourself, other individuals, or organization

--- KNOWLEDGE ---
  Mathematics (imp:4.85 lvl:6.65) — Knowledge of arithmetic, algebra, geometry, calculus, statistics, and their appl
  Education and Training (imp:3.70 lvl:4.85) — Knowledge of principles and methods for curriculum and training design, teaching
  Computers and Electronics (imp:3.50 lvl:4.95) — Knowledge of circuit boards, processors, chips, electronic equipment, and comput
  English Language (imp:3.30 lvl:4.00) — Knowledge of the structure and content of the English language including the mea
  Physics (imp:3.00 lvl:4.25) — Knowledge and prediction of physical principles, laws, their interrelationships,
  Engineering and Technology (imp:2.90 lvl:3.79) — Knowledge of the practical application of engineering science and technology. Th
  Communications and Media (imp:2.15 lvl:2.50) — Knowledge of media production, communication, and dissemination techniques and m
  Administration and Management (imp:2.05 lvl:2.55) — Knowledge of business and management principles involved in strategic planning, 
  Design (imp:2.05 lvl:1.85) — Knowledge of design techniques, tools, and principles involved in production of 
  Administrative (imp:2.00 lvl:2.05) — Knowledge of administrative and office procedures and systems such as word proce
  Customer and Personal Service (imp:1.95 lvl:2.05) — Knowledge of principles and processes for providing customer and personal servic
  Foreign Language (imp:1.90 lvl:2.05) — Knowledge of the structure and content of a foreign (non-English) language inclu
  Economics and Accounting (imp:1.80 lvl:1.65) — Knowledge of economic and accounting principles and practices, the financial mar
  Biology (imp:1.75 lvl:1.95) — Knowledge of plant and animal organisms, their tissues, cells, functions, interd
  Personnel and Human Resources (imp:1.70 lvl:1.60) — Knowledge of principles and procedures for personnel recruitment, selection, tra
  Chemistry (imp:1.63 lvl:1.70) — Knowledge of the chemical composition, structure, and properties of substances a
  Geography (imp:1.60 lvl:1.68) — Knowledge of principles and methods for describing the features of land, sea, an
  History and Archeology (imp:1.60 lvl:1.40) — Knowledge of historical events and their causes, indicators, and effects on civi
  Law and Government (imp:1.60 lvl:1.05) — Knowledge of laws, legal codes, court procedures, precedents, government regulat
  Philosophy and Theology (imp:1.55 lvl:1.50) — Knowledge of different philosophical systems and religions. This includes their 
  Telecommunications (imp:1.55 lvl:0.95) — Knowledge of transmission, broadcasting, switching, control, and operation of te
  Sales and Marketing (imp:1.50 lvl:1.20) — Knowledge of principles and methods for showing, promoting, and selling products
  Mechanical (imp:1.50 lvl:0.80) — Knowledge of machines and tools, including their designs, uses, repair, and main
  Therapy and Counseling (imp:1.50 lvl:1.20) — Knowledge of principles, methods, and procedures for diagnosis, treatment, and r
  Sociology and Anthropology (imp:1.45 lvl:0.84) — Knowledge of group behavior and dynamics, societal trends and influences, human 
  Psychology (imp:1.40 lvl:1.00) — Knowledge of human behavior and performance; individual differences in ability, 
  Transportation (imp:1.40 lvl:0.75) — Knowledge of principles and methods for moving people or goods by air, rail, sea
  Medicine and Dentistry (imp:1.37 lvl:0.58) — Knowledge of the information and techniques needed to diagnose and treat human i
  Production and Processing (imp:1.35 lvl:0.65) — Knowledge of raw materials, production processes, quality control, costs, and ot
  Public Safety and Security (imp:1.35 lvl:0.65) — Knowledge of relevant equipment, policies, procedures, and strategies to promote
  Fine Arts (imp:1.21 lvl:0.53) — Knowledge of the theory and techniques required to compose, produce, and perform
  Food Production (imp:1.00) — Knowledge of techniques and equipment for planting, growing, and harvesting food
  Building and Construction (imp:1.00) — Knowledge of materials, methods, and the tools involved in the construction or r

--- ABILITIES ---
  Mathematical Reasoning (imp:5.00 lvl:6.00) — The ability to choose the right mathematical methods or formulas to solve a prob
  Number Facility (imp:4.62 lvl:5.00) — The ability to add, subtract, multiply, or divide quickly and correctly.
  Oral Comprehension (imp:4.12 lvl:5.12) — The ability to listen to and understand information and ideas presented through 
  Written Comprehension (imp:4.12 lvl:5.12) — The ability to read and understand information and ideas presented in writing.
  Oral Expression (imp:4.12 lvl:5.12) — The ability to communicate information and ideas in speaking so others will unde
  Written Expression (imp:4.12 lvl:4.88) — The ability to communicate information and ideas in writing so others will under
  Deductive Reasoning (imp:4.00 lvl:5.00) — The ability to apply general rules to specific problems to produce answers that 
  Inductive Reasoning (imp:3.88 lvl:4.88) — The ability to combine pieces of information to form general rules or conclusion
  Information Ordering (imp:3.88 lvl:4.88) — The ability to arrange things or actions in a certain order or pattern according
  Category Flexibility (imp:3.88 lvl:4.00) — The ability to generate or use different sets of rules for combining or grouping
  Fluency of Ideas (imp:3.75 lvl:4.75) — The ability to come up with a number of ideas about a topic (the number of ideas
  Originality (imp:3.75 lvl:4.75) — The ability to come up with unusual or clever ideas about a given topic or situa
  Problem Sensitivity (imp:3.75 lvl:3.88) — The ability to tell when something is wrong or is likely to go wrong. It does no
  Near Vision (imp:3.62 lvl:3.75) — The ability to see details at close range (within a few feet of the observer).
  Flexibility of Closure (imp:3.25 lvl:3.75) — The ability to identify or detect a known pattern (a figure, object, word, or so
  Selective Attention (imp:3.12 lvl:3.00) — The ability to concentrate on a task over a period of time without being distrac
  Speech Clarity (imp:3.12 lvl:3.12) — The ability to speak clearly so others can understand you.
  Speech Recognition (imp:3.00 lvl:3.00) — The ability to identify and understand the speech of another person.
  Memorization (imp:2.88 lvl:2.88) — The ability to remember information such as words, numbers, pictures, and proced
  Speed of Closure (imp:2.88 lvl:3.38) — The ability to quickly make sense of, combine, and organize information into mea
  Perceptual Speed (imp:2.88 lvl:2.88) — The ability to quickly and accurately compare similarities and differences among
  Visualization (imp:2.75 lvl:2.88) — The ability to imagine how something will look after it is moved around or when 
  Far Vision (imp:2.00 lvl:2.25) — The ability to see details at a distance.
  Time Sharing (imp:1.88 lvl:1.50) — The ability to shift back and forth between two or more activities or sources of
  Visual Color Discrimination (imp:1.88 lvl:0.88) — The ability to match or detect differences between colors, including shades of c
  Trunk Strength (imp:1.75 lvl:1.00) — The ability to use your abdominal and lower back muscles to support part of the 
  Hearing Sensitivity (imp:1.62 lvl:0.75) — The ability to detect or tell the differences between sounds that vary in pitch 
  Auditory Attention (imp:1.62 lvl:0.75) — The ability to focus on a single source of sound in the presence of other distra
  Finger Dexterity (imp:1.50 lvl:1.00) — The ability to make precisely coordinated movements of the fingers of one or bot
  Depth Perception (imp:1.38 lvl:0.38) — The ability to judge which of several objects is closer or farther away from you
  Wrist-Finger Speed (imp:1.25 lvl:0.25) — The ability to make fast, simple, repeated movements of the fingers, hands, and 
  Spatial Orientation (imp:1.12 lvl:0.12) — The ability to know your location in relation to the environment or to know wher
  Arm-Hand Steadiness (imp:1.00) — The ability to keep your hand and arm steady while moving your arm or while hold
  Manual Dexterity (imp:1.00) — The ability to quickly move your hand, your hand together with your arm, or your
  Control Precision (imp:1.00) — The ability to quickly and repeatedly adjust the controls of a machine or a vehi
  Multilimb Coordination (imp:1.00) — The ability to coordinate two or more limbs (for example, two arms, two legs, or
  Response Orientation (imp:1.00) — The ability to choose quickly between two or more movements in response to two o
  Rate Control (imp:1.00) — The ability to time your movements or the movement of a piece of equipment in an
  Reaction Time (imp:1.00) — The ability to quickly respond (with the hand, finger, or foot) to a signal (sou
  Speed of Limb Movement (imp:1.00) — The ability to quickly move the arms and legs.
  Static Strength (imp:1.00) — The ability to exert maximum muscle force to lift, push, pull, or carry objects.
  Explosive Strength (imp:1.00) — The ability to use short bursts of muscle force to propel oneself (as in jumping
  Dynamic Strength (imp:1.00) — The ability to exert muscle force repeatedly or continuously over time. This inv
  Stamina (imp:1.00) — The ability to exert yourself physically over long periods of time without getti
  Extent Flexibility (imp:1.00) — The ability to bend, stretch, twist, or reach with your body, arms, and/or legs.
  Dynamic Flexibility (imp:1.00) — The ability to quickly and repeatedly bend, stretch, twist, or reach out with yo
  Gross Body Coordination (imp:1.00) — The ability to coordinate the movement of your arms, legs, and torso together wh
  Gross Body Equilibrium (imp:1.00) — The ability to keep or regain your body balance or stay upright when in an unsta
  Night Vision (imp:1.00) — The ability to see under low-light conditions.
  Peripheral Vision (imp:1.00) — The ability to see objects or movement of objects to one's side when the eyes ar
  Glare Sensitivity (imp:1.00) — The ability to see objects in the presence of a glare or bright lighting.
  Sound Localization (imp:1.00) — The ability to tell the direction from which a sound originated.

--- WORK ACTIVITIES ---
  Thinking Creatively (imp:4.70 lvl:6.55) — Developing, designing, or creating new applications, ideas, relationships, syste
  Analyzing Data or Information (imp:4.55 lvl:6.30) — Identifying the underlying principles, reasons, or facts of information by break
  Updating and Using Relevant Knowledge (imp:4.35 lvl:6.05) — Keeping up-to-date technically and applying new knowledge to your job.
  Processing Information (imp:4.30 lvl:6.10) — Compiling, coding, categorizing, calculating, tabulating, auditing, or verifying
  Working with Computers (imp:4.25 lvl:4.90) — Using computers and computer systems (including hardware and software) to progra
  Training and Teaching Others (imp:4.25 lvl:5.65) — Identifying the educational needs of others, developing formal educational or tr
  Making Decisions and Solving Problems (imp:4.20 lvl:5.30) — Analyzing information and evaluating results to choose the best solution and sol
  Getting Information (imp:4.15 lvl:5.70) — Observing, receiving, and otherwise obtaining information from all relevant sour
  Interpreting the Meaning of Information for Others (imp:3.95 lvl:5.60) — Translating or explaining what information means and how it can be used.
  Communicating with Supervisors, Peers, or Subordinates (imp:3.50 lvl:4.80) — Providing information to supervisors, co-workers, and subordinates by telephone,
  Organizing, Planning, and Prioritizing Work (imp:3.45 lvl:4.60) — Developing specific goals and plans to prioritize, organize, and accomplish your
  Coaching and Developing Others (imp:3.42 lvl:4.25) — Identifying the developmental needs of others and coaching, mentoring, or otherw
  Documenting/Recording Information (imp:3.35 lvl:3.90) — Entering, transcribing, recording, storing, or maintaining information in writte
  Estimating the Quantifiable Characteristics of Products, Events, or Information (imp:3.25 lvl:4.15) — Estimating sizes, distances, and quantities; or determining time, costs, resourc
  Developing Objectives and Strategies (imp:3.25 lvl:4.25) — Establishing long-range objectives and specifying the strategies and actions to 
  Communicating with People Outside the Organization (imp:3.21 lvl:5.15) — Communicating with people outside the organization, representing the organizatio
  Providing Consultation and Advice to Others (imp:3.20 lvl:4.65) — Providing guidance and expert advice to management or other groups on technical,
  Establishing and Maintaining Interpersonal Relationships (imp:2.95 lvl:3.75) — Developing constructive and cooperative working relationships with others, and m
  Scheduling Work and Activities (imp:2.85 lvl:3.75) — Scheduling events, programs, and activities, as well as the work of others.
  Guiding, Directing, and Motivating Subordinates (imp:2.84 lvl:3.47) — Providing guidance and direction to subordinates, including setting performance 
  Coordinating the Work and Activities of Others (imp:2.70 lvl:3.75) — Getting members of a group to work together to accomplish tasks.
  Developing and Building Teams (imp:2.70 lvl:3.40) — Encouraging and building mutual trust, respect, and cooperation among team membe
  Identifying Objects, Actions, and Events (imp:2.65 lvl:3.10) — Identifying information by categorizing, estimating, recognizing differences or 
  Evaluating Information to Determine Compliance with Standards (imp:2.65 lvl:2.90) — Using relevant information and individual judgment to determine whether events o
  Judging the Qualities of Objects, Services, or People (imp:2.55 lvl:2.75) — Assessing the value, importance, or quality of things or people.
  Performing Administrative Activities (imp:2.30 lvl:3.11) — Performing day-to-day administrative tasks such as maintaining information files
  Selling or Influencing Others (imp:2.10 lvl:2.16) — Convincing others to buy merchandise/goods or to otherwise change their minds or
  Resolving Conflicts and Negotiating with Others (imp:2.10 lvl:2.25) — Handling complaints, settling disputes, and resolving grievances and conflicts, 
  Monitoring Processes, Materials, or Surroundings (imp:2.05 lvl:2.53) — Monitoring and reviewing information from materials, events, or the environment,
  Staffing Organizational Units (imp:2.00 lvl:1.80) — Recruiting, interviewing, selecting, hiring, and promoting employees in an organ
  Monitoring and Controlling Resources (imp:1.95 lvl:2.40) — Monitoring and controlling resources and overseeing the spending of money.
  Assisting and Caring for Others (imp:1.80 lvl:1.95) — Providing personal assistance, medical attention, emotional support, or other pe
  Inspecting Equipment, Structures, or Materials (imp:1.70 lvl:1.40) — Inspecting equipment, structures, or materials to identify the cause of errors o
  Performing for or Working Directly with the Public (imp:1.70 lvl:1.75) — Performing for people or dealing directly with the public. This includes serving
  Repairing and Maintaining Electronic Equipment (imp:1.45 lvl:1.15) — Servicing, repairing, calibrating, regulating, fine-tuning, or testing machines,
  Handling and Moving Objects (imp:1.30 lvl:1.05) — Using hands and arms in handling, installing, positioning, and moving materials,
  Controlling Machines and Processes (imp:1.30 lvl:0.70) — Using either control mechanisms or direct physical activity to operate machines 
  Drafting, Laying Out, and Specifying Technical Devices, Parts, and Equipment (imp:1.30 lvl:0.65) — Providing documentation, detailed instructions, drawings, or specifications to t
  Repairing and Maintaining Mechanical Equipment (imp:1.25 lvl:0.50) — Servicing, repairing, adjusting, and testing machines, devices, moving parts, an
  Performing General Physical Activities (imp:1.20 lvl:0.35) — Performing general physical activities includes doing activities that require co
  Operating Vehicles, Mechanized Devices, or Equipment (imp:1.10 lvl:0.15) — Running, maneuvering, navigating, or driving vehicles or mechanized equipment, s

--- WORK STYLES ---
  Attention to Detail (imp:5.00) — A tendency to be detail-oriented, organized, and thorough in completing work.
  Intellectual Curiosity (imp:4.00) — A tendency to seek out and acquire new work-related knowledge and obtain a deep 
  Achievement Orientation (imp:3.00) — A tendency to establish and maintain personally challenging work-related goals, 
  Intellectual Curiosity (imp:3.00) — A tendency to seek out and acquire new work-related knowledge and obtain a deep 
  Attention to Detail (imp:3.00) — A tendency to be detail-oriented, organized, and thorough in completing work.
  Innovation (imp:2.51) — A tendency to be inventive, to be imaginative, and to adopt new perspectives on 
  Achievement Orientation (imp:2.14) — A tendency to establish and maintain personally challenging work-related goals, 
  Perseverance (imp:2.08) — A tendency to exhibit determination and resolve to perform or complete tasks in 
  Perseverance (imp:2.00) — A tendency to exhibit determination and resolve to perform or complete tasks in 
  Dependability (imp:1.98) — A tendency to be reliable, responsible, and consistent in meeting work-related o
  Tolerance for Ambiguity (imp:1.97) — A tendency to be comfortable with ambiguity and uncertainty at work.
  Cautiousness (imp:1.82) — A tendency to be careful, deliberate, and risk-avoidant when making work-related
  Integrity (imp:1.70) — A tendency to be honest and ethical at work.
  Initiative (imp:1.47) — A tendency to be proactive and take on extra responsibilities and tasks that may
  Self-Confidence (imp:1.32) — A tendency to believe in one's work-related capabilities and ability to control 
  Adaptability (imp:1.26) — A tendency to be open to and comfortable with change, new experiences, or ideas 
  Innovation (imp:1.00) — A tendency to be inventive, to be imaginative, and to adopt new perspectives on 
  Stress Tolerance (imp:0.86) — A tendency to cope and function effectively in stressful situations at work.
  Cooperation (imp:0.55) — A tendency to be pleasant, helpful, and willing to assist others at work.
  Self-Control (imp:0.44) — A tendency to remain calm and composed and to manage emotions effectively in res
  Humility (imp:0.34) — A tendency to be modest and humble when interacting with others at work.
  Sincerity (imp:0.23) — A tendency to be genuine and sincere in interactions with others at work, withou
  Optimism (imp:0.15) — A tendency to exhibit a positive attitude and positive emotions at work, even un
  Social Orientation (imp:0.04) — A tendency to seek out, enjoy, and be energized by social interaction at work.
  Tolerance for Ambiguity () — A tendency to be comfortable with ambiguity and uncertainty at work.
  Initiative () — A tendency to be proactive and take on extra responsibilities and tasks that may
  Adaptability () — A tendency to be open to and comfortable with change, new experiences, or ideas 
  Self-Confidence () — A tendency to believe in one's work-related capabilities and ability to control 
  Leadership Orientation () — A tendency to lead, take charge, offer opinions, and provide direction at work.
  Humility () — A tendency to be modest and humble when interacting with others at work.
  Sincerity () — A tendency to be genuine and sincere in interactions with others at work, withou
  Empathy () — A tendency to show concern for others and be sensitive to others' needs and feel
  Cooperation () — A tendency to be pleasant, helpful, and willing to assist others at work.
  Optimism () — A tendency to exhibit a positive attitude and positive emotions at work, even un
  Social Orientation () — A tendency to seek out, enjoy, and be energized by social interaction at work.
  Cautiousness () — A tendency to be careful, deliberate, and risk-avoidant when making work-related
  Dependability () — A tendency to be reliable, responsible, and consistent in meeting work-related o
  Integrity () — A tendency to be honest and ethical at work.
  Stress Tolerance () — A tendency to cope and function effectively in stressful situations at work.
  Self-Control () — A tendency to remain calm and composed and to manage emotions effectively in res
  Empathy (imp:-0.03) — A tendency to show concern for others and be sensitive to others' needs and feel
  Leadership Orientation (imp:-0.09) — A tendency to lead, take charge, offer opinions, and provide direction at work.

--- TRANSFERABLE SKILLS ---
  Complex Problem Solving (imp:4.00 lvl:4.88) — Identifying complex problems and reviewing related information to develop and ev
  Judgment and Decision Making (imp:3.75 lvl:4.00) — Considering the relative costs and benefits of potential actions to choose the m
  Instructing (imp:3.00 lvl:3.88) — Teaching others how to do something.
  Systems Analysis (imp:3.00 lvl:3.75) — Determining how a system should work and how changes in conditions, operations, 
  Systems Evaluation (imp:3.00 lvl:3.62) — Identifying measures or indicators of system performance and the actions needed 
  Social Perceptiveness (imp:2.88 lvl:3.00) — Being aware of others' reactions and understanding why they react as they do.
  Coordination (imp:2.88 lvl:3.00) — Adjusting actions in relation to others' actions.
  Persuasion (imp:2.75 lvl:2.88) — Persuading others to change their minds or behavior.
  Time Management (imp:2.75 lvl:3.00) — Managing one's own time and the time of others.
  Operations Analysis (imp:2.50 lvl:2.62) — Analyzing needs and product requirements to create a design.
  Programming (imp:2.50 lvl:2.75) — Writing computer programs for various purposes.
  Negotiation (imp:2.00 lvl:1.88) — Bringing others together and trying to reconcile differences.
  Service Orientation (imp:2.00 lvl:1.75) — Actively looking for ways to help people.
  Management of Personnel Resources (imp:2.00 lvl:2.12) — Motivating, developing, and directing people as they work, identifying the best 
  Technology Design (imp:1.62 lvl:0.62) — Generating or adapting equipment and technology to serve user needs.
  Management of Financial Resources (imp:1.62 lvl:0.62) — Determining how money will be spent to get the work done, and accounting for the
  Management of Material Resources (imp:1.62 lvl:0.62) — Obtaining and seeing to the appropriate use of equipment, facilities, and materi
  Quality Control Analysis (imp:1.50 lvl:0.50) — Conducting tests and inspections of products, services, or processes to evaluate
  Operations Monitoring (imp:1.38 lvl:0.38) — Watching gauges, dials, or other indicators to make sure a machine is working pr
  Equipment Selection (imp:1.00) — Determining the kind of tools and equipment needed to do a job.
  Installation (imp:1.00) — Installing equipment, machines, wiring, or programs to meet specifications.
  Operation and Control (imp:1.00) — Controlling operations of equipment or systems.
  Equipment Maintenance (imp:1.00) — Performing routine maintenance on equipment and determining when and what kind o
  Troubleshooting (imp:1.00) — Determining causes of operating errors and deciding what to do about it.
  Repairing (imp:1.00) — Repairing machines or systems using the needed tools.

--- NATIONAL WAGES ---
  total_employment : 2,030
  annual_median    : $126,710
  annual_pct10     : $69,240
  annual_pct25     : $88,570
  annual_pct75     : $157,020
  annual_pct90     : $195,190
  annual_mean      : $129,260
  hourly_median    : $60.92

--- GEOGRAPHIC DISPERSION ---
  highest_state    : Washington ($162,280)
  lowest_state     : Michigan ($65,510)
  dispersion_ratio : 2.477x

--- TOP STATES BY WAGE (12 total) ---
  Federal, State, and Local Government, excluding State and Local Government Schools and Hospitals and the U.S. Postal Service (OEWS Designation) emp:    1,150  median: $ 134,160
  Professional, Scientific, and Technical Services emp:      270  median: $ 140,660
  Manufacturing                            emp:      130  median: $ 140,740
  Management of Companies and Enterprises  emp:       30  median: $ 132,530

--- TOP INDUSTRIES BY EMPLOYMENT (4 total) ---
  Federal, State, and Local Government, excluding State and Local Government Schools and Hospitals and the U.S. Postal Service (OEWS Designation) emp:    1,150  median: $ 134,160
  Professional, Scientific, and Technical Services emp:      270  median: $ 140,660
  Manufacturing                            emp:      130  median: $ 140,740
  Management of Companies and Enterprises  emp:       30  median: $ 132,530

exact_match_status : found
matched_title      : Mathematician
match_score        : 0.9630
wikidata_qid       : Q170790
word_count         : 2,124
wikipedia_url      : https://en.wikipedia.org/wiki/Mathematician
license            : CC BY-SA 4.0
fetched_at         : 2026-06-02T20:26:17.724587Z

--- WIKIPEDIA FULL TEXT ---
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.


== History ==

One of the earliest known mathematicians was Thales of Miletus (c. 624 – c. 546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem.
The number of known mathematicians grew when Pythagoras of Samos (c. 582 – c. 507 BC) established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number".
Archimedes was one of the greatest figures in the history of mathematics. He made significant contributions to geometry, providing proofs for the area of a circle and the volume and surface area of a sphere. He also gave a good approximation of π using polygons. He also developed the method of exhaustion, which is an early form of integral calculus. He furthered the study of centers of mass and mathematical statics. His precise methods had a strong impact on later mathematics and mathematical physics. Euclid and Apollonius were prominent ancient Greek mathematicians, with Euclid's Elements establishing geometry through axioms and logical proofs and laying the foundation of the axiomatic method, while Apollonius' Conics systematically developed the theory of ellipses, parabolas, and hyperbolas, significantly advancing the study of curves and influencing later geometry.
The first woman mathematician recorded by history was Hypatia of Alexandria (c. AD 350 – 415). She succeeded her father as librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles).
Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based primarily on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, and it turned out that certain scholars became experts in the works they translated, and in turn received further support for continuing to develop certain sciences. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support was Al-Khawarizmi. A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham.
Noteworthy Indian mathematicians from this time period include Aryabhata, who applied trigonometry to astronomy; Brahmagupta, credited with the first systematic explanation of negative numbers and zero; and the mathematician and astronomer Bhāskara II. Mādhava of Sangamagrāma is considered to be the founder of the Kerala school of astronomy and mathematics in the Late Middle Ages. He made pioneering contributions to the study of infinite series, trigonometry, geometry and algebra.
The Renaissance brought an increased emphasis on mathematics and science to Europe. During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer).
As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, and at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the "regurgitation of knowledge" to "encourag[ing] productive thinking." In 1810, Alexander von Humboldt convinced the king of Prussia, Fredrick William III, to build a university in Berlin based on Friedrich Schleiermacher's liberal ideas; the goal was to demonstrate the process of the discovery of knowledge and to teach students to "take account of fundamental laws of science in all their thinking." Thus, seminars and laboratories started to evolve.
British universities of this period adopted some approaches familiar to the Italian and German universities, but as they already enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt. The Universities of Oxford and Cambridge emphasized the importance of research, arguably more authentically implementing Humboldt's idea of a university than even German universities, which were subject to state authority. Overall, science (including mathematics) became the focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. The German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of "freedom of scientific research, teaching and study."


== Required education ==
Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then proceed to specialize in topics of their own choice at the graduate level. In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a doctoral dissertation.


== Activities ==


=== Applied mathematics ===

Mathematicians involved with solving problems with applications in real life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, and localized constructs, applied mathematicians work regularly in the study and formulation of mathematical models. Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers.
The discipline of applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics" is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on problems, often concrete but sometimes abstract. As professionals focused on problem solving, applied mathematicians look into the formulation, study, and use of mathematical models in science, engineering, business, and other areas of mathematical practice.


=== Pure mathematics ===

Pure mathematics is mathematics th

--- SEMANTIC NEIGHBORS (5) ---

  Title: List of International Congresses of Mathematicians Plenary and Invited Speakers (similarity: 0.3011)
  URL: https://en.wikipedia.org/wiki/List_of_International_Congresses_of_Mathematicians_Plenary_and_Invited_Speakers
  QID: Q21015854
  Extract: 
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." The current list of Plenary and Invited Speakers pr

  Title: List of films about mathematicians (similarity: 0.5833)
  URL: https://en.wikipedia.org/wiki/List_of_films_about_mathematicians
  QID: Q6619927
  Extract: 
This is a list of feature films and documentaries that include mathematicians, scientists who use math or references to mathematicians.

  Title: Agent-based model (similarity: 0.1290)
  URL: https://en.wikipedia.org/wiki/Agent-based_model
  QID: Q392811
  Extract: An agent-based model (ABM) is a computational model for simulating the actions and interactions of an autonomous agent to understand the behavior of a system and what governs its outcomes. It combines elements of game theory, complex systems, emergence, computational sociology, multi-agent systems, 

  Title: Intelligent agent (similarity: 0.1290)
  URL: https://en.wikipedia.org/wiki/Intelligent_agent
  QID: Q1142726
  Extract: In artificial intelligence, an intelligent agent is an entity that perceives its environment, takes actions autonomously to achieve goals, and may improve its performance through machine learning or by acquiring knowledge. AI textbooks define artificial intelligence as the "study and design of intel

  Title: Comparison of agent-based modeling software (similarity: 0.2105)
  URL: https://en.wikipedia.org/wiki/Comparison_of_agent-based_modeling_software
  QID: Q4438340
  Extract: The agent-based modeling (ABM) community has developed several practical agent based modeling toolkits that enable individuals to develop agent-based applications. More and more such toolkits are coming into existence, and each toolkit has a variety of characteristics. Several individuals have made 

model_pass1          : claude-sonnet-4-20250514
model_pass2          : claude-haiku-4-5-20251001
inference_confidence : high
confidence_notes     : Strong confidence supported by comprehensive O*NET data, clear Wikipedia match, substantial wage data from BLS OEWS, and well-defined educational pathways and related occupations.
inferred_at          : 2026-06-03T14:15:15.498996+00:00
tokens_input         : 4,428
tokens_output        : 4,199
cost_usd             : $0.045698
wikipedia_used       : True
wikipedia_title      : Mathematician
wikipedia_note       : The Wikipedia definition aligns closely with O*NET data, emphasizing the use of extensive mathematical knowledge to solve problems and work with numbers, data, quantity, structure, space, models, and change.

--- PROSE FIELDS ---

ROLE SUMMARY:
Mathematicians conduct research in fundamental mathematics and apply mathematical techniques to solve problems across science, management, and other fields. They develop new mathematical principles, create models for analysis and simulation, and advance mathematical knowledge through rigorous research and computation. With the highest level of educational preparation required, they work primarily in government, research institutions, and technical consulting.

DAY IN THE LIFE:
A mathematician spends significant time thinking creatively about mathematical problems, developing new principles and relationships between existing mathematical concepts. They perform complex computations using numerical analysis methods, create mathematical or statistical models of real-world phenomena, and analyze large datasets to identify patterns and relationships. Much of their work involves writing research papers, presenting findings at professional conferences, and collaborating with scientists and technical specialists. They also mentor others on mathematical techniques and stay current by reading professional journals and attending conferences.

WHO THRIVES:
This role attracts individuals with exceptional investigative and conventional interests who excel at abstract reasoning and complex problem-solving. Successful mathematicians possess extraordinary attention to detail and intellectual curiosity, combined with high achievement orientation. They thrive on independent research and theoretical work, requiring exceptional mathematical reasoning abilities and number facility. The role demands individuals who can work with minimal supervision on long-term projects and communicate complex mathematical concepts both orally and in writing.

CAREER ENTRY:
Entry requires extensive preparation, typically a doctoral degree (45% of practitioners) or at minimum a master's degree (25%). The educational path involves advanced study in pure mathematics, applied mathematics, statistics, or related quantitative fields. Most positions require demonstrated research capability through thesis work or published papers. Some applied mathematician roles in industry may accept candidates with strong master's-level preparation plus relevant experience.

CAREER TRAJECTORY:
Mathematicians can advance into senior research positions, department leadership roles in government agencies or research institutions, or transition into related fields like data science or quantitative analysis. Many pursue academic careers as mathematical science teachers at the postsecondary level. The strong analytical foundation also enables moves into specialized areas like cryptography, operations research, or computational science roles in technology companies.

MARKET INTELLIGENCE:
The field offers strong compensation with median annual wages of $126,710 (BLS OEWS May 2025), though employment is limited to approximately 2,030 positions nationwide. Geographic variation is significant, with Washington state offering the highest wages at $162,280 compared to Michigan at $65,510. The federal government employs the majority (1,150 positions), followed by professional and technical services. Demand is concentrated in areas with major research institutions and government facilities.

AUTOMATION OUTLOOK:
Mathematicians face low automation risk due to their focus on creative thinking, developing new mathematical principles, and solving novel problems. While computational tools enhance their work efficiency, the core activities of theoretical research, model development, and creative problem-solving require human insight and mathematical intuition that cannot be automated.

--- REASONED EDGES ---
  [skill_overlap] Data Scientists (15-2051.00) — confidence:high
    reasoning: Both roles share high-level mathematics knowledge (4.8+ importance) and mathematical reasoning abilities (5.0+ importance), with substantial overlap in data analysis activities.
    data: Mathematics knowledge importance 4.8
    data: Mathematical Reasoning ability 5.0
    data: Analyzing Data work activity 4.5+
  [knowledge_overlap] Statisticians (15-2041.00) — confidence:high
    reasoning: Strong overlap in mathematics knowledge and statistical modeling capabilities, with both developing mathematical models for analysis and computational simulation.
    data: Mathematics knowledge level 6.7
    data: Mathematical model development tasks
    data: Quantitative analysis focus
  [riasec_cluster] Physicists (19-2012.00) — confidence:high
    reasoning: Both occupations show strong investigative interests (I:7.00 for mathematicians) and apply mathematical principles to scientific problems.
    data: RIASEC Investigative 7.00
    data: Physics knowledge 3.0 importance
    data: Scientific application tasks
  [career_pathway] Mathematical Science Teachers, Postsecondary (25-1022.00) — confidence:high
    reasoning: Natural progression given education requirements (45% doctoral degrees) and training/teaching activities (importance 4.2) in current mathematician roles.
    data: Doctoral degree 45%
    data: Training and Teaching Others 4.2 importance
    data: Education and Training knowledge 3.7
  [task_similarity] Computer and Information Research Scientists (15-1221.00) — confidence:medium
    reasoning: Both roles involve developing computational models and simulations, with mathematicians showing high computer work activity (4.2 importance) and technology tool usage.
    data: Working with Computers 4.2 importance
    data: Computational simulation tasks
    data: Programming languages in hot technology
  [transferable_skill] Operations Research Analysts (15-2031.00) — confidence:medium
    reasoning: Shared systems analysis and complex problem-solving transferable skills, with both applying mathematical methods to practical business problems.
    data: Complex Problem Solving transferable skill 4.0
    data: Systems Analysis 3.0
    data: Practical business application tasks
  [job_zone] Mathematicians (15-2021.00) — confidence:high
    reasoning: All related occupations requiring Job Zone 5 preparation share similar extensive educational and experience requirements.
    data: Job Zone 5 classification
    data: Doctoral degree requirements
    data: Extensive preparation needed

--- NORMALIZER SIGNALS ---
  match_keywords   : ['mathematician', 'mathematical research', 'pure mathematics', 'applied mathematics', 'mathematical modeling', 'theoretical mathematics', 'mathematical analysis', 'computational mathematics']
  exclude_keywords : ['teacher', 'professor', 'instructor', 'educator', 'tutor']
  title_patterns   : ['mathematician', 'research mathematician', 'applied mathematician', 'computational mathematician', 'mathematical researcher']
  common_variations: ['mathematician', 'mathematical researcher', 'math researcher', 'research mathematician', 'applied mathematician', 'computational mathematician', 'mathematical scientist', 'mathematical analyst']

total_terms    : 40
top_words      : ['mathematics', 'mathematical', 'tendency', 'others', 'mathematicians', 'research', 'mathematician', 'equipment', 'principles', 'problems', 'applied', 'science', 'techniques', 'models', 'many', 'includes', 'control', 'ideas', 'objects', 'activities']
source_layers  : onet_tasks | onet_dimensions | dwas | wikipedia | inference

TERM                    COUNT     FREQ  DOMINANT SOURCE      SOURCE BREAKDOWN
──────────────────────────────────────────────────────────────────────────────────────────
mathematics                49  0.01306  wikipedia            wikipedia:88%  onet_dimensions:6%  inference:6%
mathematical               47  0.01253  wikipedia            wikipedia:49%  inference:28%  onet_tasks:13%
tendency                   42  0.01120  onet_dimensions      onet_dimensions:100%
others                     41  0.01093  onet_dimensions      onet_dimensions:93%  onet_tasks:2%  dwas:2%
mathematicians             40  0.01066  wikipedia            wikipedia:88%  inference:10%  onet_tasks:2%
research                   25  0.00666  inference            inference:44%  wikipedia:36%  onet_tasks:8%
mathematician              24  0.00640  wikipedia            wikipedia:92%  inference:8%
equipment                  23  0.00613  onet_dimensions      onet_dimensions:100%
principles                 22  0.00587  onet_dimensions      onet_dimensions:73%  inference:14%  onet_tasks:9%
problems                   22  0.00587  onet_dimensions      onet_dimensions:41%  wikipedia:27%  inference:18%
applied                    20  0.00533  wikipedia            wikipedia:85%  inference:10%  dwas:5%
science                    17  0.00453  wikipedia            wikipedia:53%  inference:24%  onet_tasks:12%
techniques                 15  0.00400  onet_dimensions      onet_dimensions:67%  onet_tasks:13%  inference:13%
models                     15  0.00400  wikipedia            wikipedia:60%  inference:20%  onet_tasks:7%
many                       13  0.00347  wikipedia            wikipedia:92%  inference:8%
includes                   12  0.00320  onet_dimensions      onet_dimensions:100%
control                    12  0.00320  onet_dimensions      onet_dimensions:100%
ideas                      12  0.00320  onet_dimensions      onet_dimensions:92%  wikipedia:8%
objects                    12  0.00320  onet_dimensions      onet_dimensions:100%
activities                 12  0.00320  onet_dimensions      onet_dimensions:75%  dwas:8%  wikipedia:8%
study                      12  0.00320  wikipedia            wikipedia:92%  inference:8%
prize                      12  0.00320  wikipedia            wikipedia:100%
financial                  11  0.00293  wikipedia            wikipedia:64%  onet_dimensions:27%  onet_tasks:9%
scientific                 11  0.00293  wikipedia            wikipedia:73%  dwas:18%  onet_dimensions:9%
relationships              10  0.00267  onet_dimensions      onet_dimensions:30%  dwas:30%  onet_tasks:20%
analysis                   10  0.00267  onet_dimensions      onet_dimensions:40%  inference:30%  onet_tasks:20%
solving                    10  0.00267  onet_dimensions      onet_dimensions:40%  inference:30%  wikipedia:20%
design                     10  0.00267  onet_dimensions      onet_dimensions:60%  wikipedia:20%  onet_tasks:10%
problem                    10  0.00267  onet_dimensions      onet_dimensions:70%  inference:20%  wikipedia:10%
teaching                   10  0.00267  onet_dimensions      onet_dimensions:50%  wikipedia:50%
human                      10  0.00267  onet_dimensions      onet_dimensions:70%  wikipedia:20%  inference:10%
resources                  10  0.00267  onet_dimensions      onet_dimensions:90%  wikipedia:10%
materials                  10  0.00267  onet_dimensions      onet_dimensions:100%
actions                    10  0.00267  onet_dimensions      onet_dimensions:80%  wikipedia:20%
body                       10  0.00267  onet_dimensions      onet_dimensions:100%
orientation                10  0.00267  onet_dimensions      onet_dimensions:90%  inference:10%
developing                 10  0.00267  onet_dimensions      onet_dimensions:80%  inference:20%
universities               10  0.00267  wikipedia            wikipedia:100%
agent                      10  0.00267  wikipedia            wikipedia:100%
writing                     9  0.00240  onet_dimensions      onet_dimensions:67%  inference:22%  onet_tasks:11%