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Mathematicians

SOC 15-2021.00Job Zone 5 · Extensive Preparationv.26.05

Context coveredThis framework covers theoretical and applied mathematical research, computational analysis, scholarly dissemination, and mentorship performed in academic, government laboratory, and industry R&D environments by practitioners holding advanced degrees.

Sources:O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.SkillsCrosswalkSkillsCrosswalk — O*NET enrichment + adjacency index. Opens in new tab.
Emerging
Entry / Apprentice
  1. Mathematical notation and symbolic representations — apply to address relationships between quantities, magnitudes, and forms under faculty or senior mathematician guidance.
  2. Numerical analysis methods — execute standard computations on structured datasets within a supervised research or academic laboratory setting.
  3. Professional journals and conference proceedings — review regularly to build foundational awareness of current developments in assigned mathematical subdisciplines.
  4. Algebraic and geometric principles — investigate known relationships and reproduce established proofs under the direction of a research supervisor.
  5. Analytical or scientific software tools — operate to support assigned computational tasks within a university or government research environment.
  6. Sets of assumptions — assemble under supervision and enumerate immediate logical consequences for well-defined, bounded mathematical problems.
  7. Research findings — summarize in written draft reports following established conventions for internal review by a supervising mathematician.
  8. Undergraduate or early graduate students — assist in tutoring sessions on mathematical techniques under the oversight of a lead instructor.
  9. Object-oriented and development environment software — utilize to implement basic algorithms supporting mathematical research tasks.
  10. Literature in traditional areas such as probability and logic — read and synthesize to identify gaps relevant to an assigned research project.
Developing
Mid-level / Established
  1. Computations and numerical analysis methods — perform independently on moderately complex datasets within applied research or industry analytical environments.
  2. Relationships between quantities and mathematical forms — explore and document using symbolic reasoning with routine oversight on multi-phase research projects.
  3. Research contributions — disseminate by drafting and submitting papers to peer-reviewed journals or presenting findings at professional conferences.
  4. Algebraic, geometric, and probabilistic frameworks — apply to extend established results in focused research problems with limited senior direction.
  5. Assumption sets for mathematical models — construct and systematically evaluate competing consequences in support of ongoing institutional research.
  6. Professional conferences and peer networks — engage with regularly to stay current and incorporate emerging techniques into daily research practice.
  7. Junior researchers or graduate students — mentor on core mathematical techniques and software tools within a laboratory or departmental setting.
  8. Analytical and scientific software platforms — configure and adapt to address non-standard computational problems arising in research workflows.
  9. Technical reports and research papers — write with clear argumentation and precise notation suitable for submission to domain-specific publications.
  10. Systems of mathematical relationships — analyze using deductive and inductive reasoning to validate model assumptions in applied or theoretical contexts.
Proficient
Senior / Expert IC
  1. New mathematical principles and inter-domain relationships — develop autonomously to advance knowledge in areas such as algebra, topology, or stochastic analysis.
  2. Complex, non-routine mathematical problems — solve across the full research lifecycle from problem formulation through proof or computational verification.
  3. Research dissemination strategy — execute by publishing in high-impact journals, delivering invited conference presentations, and contributing to edited volumes.
  4. Comprehensive assumption sets for novel models — assemble and rigorously explore all consequence branches, identifying theoretical boundaries and failure modes.
  5. Numerical analysis and advanced computational methods — apply at scale to large, ambiguous datasets within cross-disciplinary research or industrial R&D environments.
  6. Graduate students and early-career mathematicians — mentor on specialized mathematical techniques, proof strategies, and professional research practice.
  7. Emerging literature across mathematics, physics, and computer science — critically synthesize to identify convergences that open new research directions.
  8. Analytical software, scientific computing platforms, and programming environments — integrate to build reproducible, high-performance mathematical research pipelines.
  9. Oral and written communication of advanced mathematical results — tailor for diverse audiences ranging from specialist peers to interdisciplinary collaborators.
  10. Evaluation of mathematical systems and models — conduct using systems analysis and monitoring methods to assess correctness, scalability, and applicability.
Advanced
Lead / Principal / Executive
  1. Field-level research agenda — define and champion across institutional, funding, and international scholarly communities to shape the trajectory of a mathematical discipline.
  2. Novel theoretical frameworks connecting previously unrelated mathematical domains — originate and validate, producing results with broad scientific impact.
  3. Doctoral researchers and postdoctoral fellows — develop through sustained mentorship, personalized learning strategies, and integration into high-visibility research programs.
  4. Institutional research programs — lead by securing major grants, forming cross-sector partnerships, and aligning mathematical inquiry with national or global priorities.
  5. Peer-reviewed publications, monographs, and keynote addresses — produce at an authoritative level that establishes citation-defining contributions to mathematical science.
  6. Complex assumption-driven models addressing high-stakes real-world problems — architect and oversee from theoretical design through computational deployment in government or industry.
  7. Cross-disciplinary collaboration frameworks — establish between mathematics departments and fields such as physics, computer science, and engineering to accelerate applied innovation.
  8. Organizational knowledge-management systems and research workflows — design and evaluate to maximize productivity and reproducibility across large mathematical research teams.
  9. Standards and best practices for mathematical education and training — develop and promulgate at curriculum, departmental, or national professional-society levels.
  10. Strategic technology adoption — guide at the organizational level by evaluating emerging analytical platforms and development environments for alignment with long-term research objectives.

AI-at-Work Competency Framework

Sources:Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab.Jadhav & Danve, 2026Skill Automation Feasibility Index — Jadhav & Danve, 2026 (arXiv:2604.06906). Opens in new tab.WEF Skills TaxonomyWEF Skills Taxonomy 2021 — Building a Common Language for Skills at Work. Opens in new tab.

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Sources:Pathsmith™ Durable SkillsPathsmith™ Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
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Related titles
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RAPIDS apprenticeships
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O*NET skills
MathematicsCritical ThinkingComplex Problem SolvingActive LearningReading ComprehensionJudgment and Decision MakingWritingScienceActive ListeningSpeakingLearning StrategiesSystems AnalysisMonitoringInstructingSystems Evaluation
Knowledge domains
MathematicsEducation and TrainingComputers and ElectronicsEnglish LanguagePhysics
Abilities
Mathematical ReasoningNumber FacilityOral ExpressionWritten ComprehensionOral ComprehensionWritten ExpressionDeductive ReasoningInductive ReasoningInformation OrderingCategory Flexibility
Work styles
Intellectual CuriosityAttention to DetailInnovationAchievement OrientationPerseveranceDependability
Technology
Graphics or photo imaging softwareAnalytical or scientific softwareOperating system softwareContent workflow softwareDevelopment environment softwareObject or component oriented development softwareWeb platform development softwareIndustrial control softwareEnterprise application integration softwareDesktop publishing software
Tasks · seed anchors for statements
  1. Mentor others on mathematical techniques.
  2. Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
  3. Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
  4. Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
  5. Assemble sets of assumptions, and explore the consequences of each set.
  6. Perform computations and apply methods of numerical analysis to data.
  7. Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
  8. Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
CIP education codes
26.119927.010127.010227.010327.010427.010527.019927.030127.030327.030427.030527.030627.039927.050227.050327.999930.080130.490130.500138.0102

Sources: O*NET v30.2 (CC BY 4.0), SkillsCrosswalk.com, LER.me®, Anthropic Economic Index, SAFI (Jadhav & Danve, 2026), WEF Skills Taxonomy 2021, Pathsmith™ Durable Skills Framework. © 2026 EBSCOed.