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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.
Subscriber feature

Authoritative source data identified for 998 occupations

How a worker at each mastery level uses, directs, and evaluates AI tools in this occupation. Each statement cites its evidence inline; click a citation chip to verify the source.

Emerging
  1. AI-assisted computation — runs symbolic and numerical calculations through an LLM or CAS-integrated AI tool for well-defined problems, cross-checking outputs against known results before accepting them Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab..
  2. Literature orientation — uses AI-powered search and summarization tools to surface relevant theorems, proofs, and prior work from professional journals, reducing time spent on manual literature review Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab..
Developing
  1. Assumption-set exploration — delegates the mechanical enumeration of consequences for a given set of axioms or constraints to an AI assistant, then critically evaluates each output for logical soundness 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..
  2. Proof-sketch drafting — directs an AI tool to generate initial proof outlines for tractable sub-problems, retaining authorship of the mathematical argument structure and verifying each step independently Jadhav & Danve, 2026Skill Automation Feasibility Index — Jadhav & Danve, 2026 (arXiv:2604.06906). Opens in new tab..
  3. Mathematical writing support — uses an AI assistant to draft and refine sections of research reports and conference papers, while personally ensuring the precision of all formal statements Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab..
Proficient
  1. Complex problem decomposition — orchestrates an AI assistant through multi-stage problem breakdowns, assigning well-scoped sub-tasks to the model and integrating results into a coherent solution framework, saving substantive working time Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab..
  2. Principle-relationship discovery — employs AI tools to generate candidate relationships between mathematical structures, then applies rigorous critical thinking to select, refine, or reject proposed connections before formal development 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..
  3. Research dissemination pipeline — coordinates AI-assisted drafting, notation checking, and formatting across manuscripts and presentations, maintaining intellectual ownership of all novel claims Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab..
  4. Mentoring augmentation — uses AI-generated examples, counterexamples, and worked solutions as instructional scaffolding when mentoring junior mathematicians, evaluating AI outputs for pedagogical accuracy before use Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab..
Advanced
  1. Autonomous research agenda direction — governs a portfolio of AI-assisted exploratory computations and conjecture-generation sessions, integrating findings into original theoretical contributions that advance mathematical science, operating in a domain where mathematics skills carry high displacement risk yet demand irreplaceable human judgment 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..
  2. AI capability boundary arbitration — evaluates which classes of mathematical tasks are safely delegable to AI versus which require human proof, setting team-level protocols for AI use in high-stakes formal reasoning contexts and communicating those standards through publications and conference presentations 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..
  3. Cross-disciplinary AI-math integration — leads collaborative projects where AI tools bridge mathematical theory and applied domains, designing the problem formulations and validation criteria that govern autonomous AI contributions within the Artificial Intelligence skill cluster WEF Skills TaxonomyWEF Skills Taxonomy 2021 — Building a Common Language for Skills at Work. Opens in new tab. Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab..
Evidence pack
AEI usage
Task observations: 6233
Augment share: 95%
Time saved: 84.1%
AI autonomy: 2.95
SAFI positioning
Top skill: Mathematics
Score: 73.2 / 100
Quadrant: Q1_high_displacement_risk
precision: exact
WEF cluster
Artificial Intelligence
artificial_intelligence
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.

Pathsmith Durable Skills Framework

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.
Subscriber feature

Ten durable-skill domains mapped to four proficiency/role levels for each occupation. Each statement is aligned to the Pathsmith taxonomy, derived from trusted grounding data and mapped to occupation-specific O*NET tasks and skills.

1Communication11 statements
Emerging
  1. Mathematical notation communication — translates basic symbolic expressions into plain-language descriptions for non-specialist audiences 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.
  2. Research summary writing — drafts introductory sections of mathematical reports using standard academic conventions 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.
Developing
  1. Proof explanation — articulates logical steps of a mathematical proof clearly to peers and students in seminar or classroom settings 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.
  2. Conference abstract writing — composes concise summaries of research findings for submission to professional mathematics conferences O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Technical vocabulary calibration — adjusts mathematical language complexity based on audience expertise during presentations or consultations Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Applying
  1. Research dissemination — presents original mathematical findings through peer-reviewed publications and conference talks, structuring arguments for expert scrutiny 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.
  2. Cross-disciplinary translation — communicates quantitative methods and mathematical models clearly to scientists, engineers, or policy stakeholders in applied project contexts O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Mentorship communication — explains advanced mathematical techniques to junior researchers or graduate students using scaffolded, step-by-step discourse O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Exceeding
  1. Field-defining publication — authors landmark papers that establish new mathematical frameworks, setting the communicative standard for terminology and notation across the discipline 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.
  2. Public mathematics advocacy — delivers accessible talks or writes for general audiences, translating abstract mathematical concepts into compelling narratives that build public understanding Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  3. Editorial and review leadership — provides authoritative written critique of submitted manuscripts, shaping the quality and direction of mathematical literature O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
2Leadership11 statements
Emerging
  1. Research group participation — contributes assigned tasks within a collaborative mathematical research team, demonstrating reliability and follow-through Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Peer mentoring initiation — assists fellow students or junior colleagues with foundational mathematical techniques under faculty or senior guidance O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Developing
  1. Project coordination — organizes sub-tasks and timelines for a defined mathematical research project, coordinating contributions from two or more collaborators Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Mentorship delivery — guides junior mathematicians or graduate students through problem-solving strategies and proof techniques with increasing autonomy O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Workshop facilitation — leads focused mathematical working sessions, setting agenda and directing technical discussion toward productive outcomes Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Applying
  1. Research program direction — defines research objectives, allocates investigative responsibilities, and drives a multi-year mathematical inquiry to publication and dissemination 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.
  2. Graduate student development — mentors doctoral candidates through dissertation research, providing sustained guidance on mathematical rigor, methodology, and professional norms O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Initiative ownership — proposes and champions new lines of mathematical inquiry within an institution or research group, securing resources and buy-in from stakeholders Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Exceeding
  1. Field stewardship — shapes the strategic direction of a mathematical subfield through editorial board service, grant panel leadership, and keynote contributions at premier conferences 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.
  2. Institution-building leadership — establishes or directs research centers, doctoral programs, or collaborative networks that expand the capacity of the mathematical sciences community Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  3. Cross-sector influence — leads interdisciplinary teams applying advanced mathematics to high-stakes domains such as national defense, public health modeling, or financial risk, translating mathematical vision into organizational outcomes O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
3Metacognition10 statements
Emerging
  1. Problem approach reflection — identifies which proof strategies or computational methods were attempted and notes where understanding broke down after completing a mathematical exercise Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Learning gap recognition — acknowledges specific deficits in mathematical knowledge areas and selects readings or coursework to address them 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.
Developing
  1. Strategy monitoring — evaluates the effectiveness of a chosen analytical approach mid-problem and pivots to an alternative method when progress stalls Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Research planning self-assessment — reviews personal progress against a defined mathematical research timeline, adjusting effort allocation based on honest evaluation of output quality Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  3. Literature-driven self-updating — tracks personal knowledge currency by systematically reading professional journals and identifying emerging areas requiring deeper study O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Applying
  1. Conjecture evaluation discipline — critically assesses own assumptions and conjectured results before committing to a proof path, reducing wasted effort through deliberate cognitive monitoring 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.
  2. Methodological repertoire awareness — maintains explicit awareness of the range of mathematical tools at one's disposal and selects among them based on reflective analysis of problem structure Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  3. Feedback integration — incorporates reviewer, collaborator, and peer critique into revised manuscripts and research directions through structured self-evaluation Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Exceeding
  1. Research epistemology modeling — articulates to students and collaborators the meta-level reasoning behind selecting mathematical frameworks, making implicit cognitive processes visible and teachable 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.
  2. Long-horizon self-direction — designs multi-year personal research agendas through honest appraisal of intellectual strengths, knowledge boundaries, and the evolving landscape of mathematical science Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
4Critical Thinking11 statements
Emerging
  1. Assumption identification — lists explicit and implicit assumptions underlying a given mathematical problem before beginning solution attempts 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.
  2. Logical validity checking — verifies that each step in a provided proof follows necessarily from prior statements using established rules of inference Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Developing
  1. Counterexample construction — generates specific counterexamples to test and potentially falsify conjectured mathematical statements 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.
  2. Evidence-based conjecture — assembles numerical or symbolic evidence to build a case for or against a mathematical hypothesis before formalizing a proof O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Methodology critique — evaluates the appropriateness of a chosen numerical or analytical method for a given problem by examining its assumptions, accuracy, and limitations 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.
Applying
  1. Consequence mapping — assembles and systematically explores the full set of logical consequences arising from a defined collection of mathematical assumptions O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Cross-area synthesis judgment — determines when results or techniques from one mathematical domain apply legitimately to problems in another, evaluating structural analogies with rigor 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.
  3. Model validity assessment — critically evaluates mathematical models used in applied contexts by examining boundary conditions, sensitivity to assumptions, and alignment with empirical data O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Exceeding
  1. Foundational assumption challenge — identifies and interrogates the axiomatic foundations of an established mathematical theory, opening new avenues of inquiry or exposing hidden constraints 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.
  2. Peer work adjudication — renders authoritative critical judgments on the correctness, novelty, and significance of others' mathematical proofs and research contributions as a reviewer or committee member 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.
  3. Paradigm evaluation — assesses competing mathematical frameworks for modeling a class of phenomena, recommending adoption, revision, or abandonment based on rigorous comparative analysis Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
5Collaboration10 statements
Emerging
  1. Research team contribution — completes assigned computational or literature tasks within a larger mathematical research project, communicating progress to team members Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Collaborative problem-solving participation — engages constructively in group problem sessions, building on others' ideas and sharing partial results without territorial behavior Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Developing
  1. Co-authorship coordination — negotiates task division, reconciles differing analytical approaches, and integrates contributions from multiple authors into a coherent mathematical manuscript 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.
  2. Interdisciplinary liaison — works with scientists or engineers to translate domain-specific questions into precise mathematical formulations, bridging professional vocabularies O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Seminar reciprocity — provides substantive, collegial feedback on peers' presented work in departmental seminars, fostering shared intellectual progress Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Applying
  1. Multi-institution research collaboration — coordinates mathematical research across geographically distributed teams, aligning methodologies and maintaining shared standards of rigor 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.
  2. Applied project partnership — collaborates with non-mathematician stakeholders to define tractable mathematical problems, deliver results, and iterate based on practical constraints O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Conflict navigation in research teams — mediates disagreements over proof strategies or publication credit through principled negotiation grounded in shared commitment to mathematical integrity Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Exceeding
  1. Collaborative network cultivation — builds and sustains long-term research partnerships across institutions and disciplines, generating mathematical work that exceeds what any single investigator could produce 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.
  2. Community infrastructure building — organizes conferences, workshops, or collaborative grants that structure productive collective inquiry across the broader mathematical sciences community O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
6Character10 statements
Emerging
  1. Attribution integrity — accurately cites prior mathematical results and acknowledges the sources of techniques used in coursework and early research contributions Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Deadline accountability — delivers assigned research tasks and report drafts on agreed timelines, communicating proactively when obstacles arise Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Developing
  1. Research honesty — reports computational results, including negative or inconclusive findings, accurately without selective omission or distortion to fit desired conclusions 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.
  2. Collegial professionalism — engages respectfully with collaborators and reviewers, maintaining constructive conduct even when receiving critical feedback on mathematical work Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  3. Conflict-of-interest transparency — discloses relevant professional relationships when serving as a reviewer, grant panelist, or expert consultant Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Applying
  1. Proof integrity — submits only rigorously verified proofs for publication, retracting or correcting errors discovered post-submission with full transparency to editors and the community 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.
  2. Mentorship ethics — maintains appropriate professional boundaries with students, advocates equitably for their development, and credits their contributions honestly in joint work 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.
  3. Data and computation accountability — documents numerical methods, assumptions, and computational procedures with sufficient detail to allow independent verification and replication O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Exceeding
  1. Field ethics modeling — publicly addresses issues of research misconduct, authorship disputes, or methodological fraud within the mathematical community, upholding professional standards at institutional or national level Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Inclusive excellence stewardship — champions equitable access to mathematical education and research careers, advocating for underrepresented groups through policy, mentorship, and institutional reform Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
7Creativity10 statements
Emerging
  1. Alternative approach exploration — attempts multiple distinct proof strategies for a single mathematical problem rather than defaulting to the first method encountered Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Analogical reasoning initiation — identifies structural similarities between an unfamiliar problem and previously solved ones, proposing novel solution pathways by analogy 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.
Developing
  1. Novel conjecture formulation — constructs original mathematical conjectures by extending known results or combining ideas from disparate areas of mathematics 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.
  2. Technique hybridization — combines methods from two or more mathematical subfields to attack problems that resist conventional single-discipline approaches Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  3. Exploratory assumption variation — systematically alters the assumptions of a known theorem to discover what new or different results emerge under modified conditions O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Applying
  1. New principle development — derives original relationships between existing mathematical concepts, advancing the theoretical foundations of a subfield through genuinely novel contributions O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Problem reformulation — reframes an intractable mathematical problem in an alternative representation or framework, making a solution path accessible for the first time 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.
  3. Applied model invention — designs original mathematical models for phenomena in physics, economics, or data science by creatively synthesizing tools from pure and applied mathematics O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Exceeding
  1. Mathematical framework creation — establishes entirely new theoretical structures—new algebras, geometries, or analytical frameworks—that open entire domains of subsequent mathematical inquiry 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.
  2. Cross-disciplinary mathematical innovation — invents mathematical tools adopted broadly across science and engineering, demonstrating creative impact that transcends the mathematics discipline itself 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.
8Growth Mindset10 statements
Emerging
  1. Proof failure learning — documents what went wrong in an unsuccessful proof attempt and uses that analysis to inform the next approach rather than abandoning the problem Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Feedback receptivity — receives critical comments on mathematical work from instructors or peers without defensiveness and incorporates suggestions into revisions Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Developing
  1. Sustained problem engagement — continues working on intractable mathematical problems over weeks or months, treating persistent difficulty as evidence of the problem's significance rather than personal inadequacy 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.
  2. New area self-study — independently learns mathematical subfields outside current expertise by engaging primary literature and attending seminars, expanding personal problem-solving repertoire 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.
  3. Conference critique integration — returns from professional conferences and incorporates audience challenges and alternative perspectives into ongoing research directions 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.
Applying
  1. Long-cycle research persistence — maintains productive engagement with a major unsolved problem across multi-year research programs, adapting strategy based on accumulated evidence while sustaining motivation 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.
  2. Computational skill updating — proactively acquires new numerical methods, programming languages, or simulation tools as the discipline evolves, treating technical obsolescence as a solvable learning challenge 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.
  3. Rejection reframing — treats rejected manuscripts as opportunities to strengthen proofs, sharpen exposition, and deepen results before resubmission to higher-impact venues Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Exceeding
  1. Paradigm-shift openness — remains willing to abandon a favored theoretical approach when evidence accumulates against it, modeling intellectual flexibility for junior researchers Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Community learning culture — institutionalizes growth-oriented norms in research groups and departments by structuring seminars, reading groups, and mentorship practices around learning from failure and iterative improvement 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.
9Mindfulness10 statements
Emerging
  1. Attention regulation in problem work — applies focused, distraction-free effort to mathematical derivations, recognizing when cognitive fatigue requires deliberate breaks and reset Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Emotional awareness under difficulty — notices frustration or discouragement arising from mathematical setbacks and pauses before responding unproductively Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Developing
  1. Deep work discipline — structures daily research time to protect sustained, uninterrupted engagement with complex mathematical problems, minimizing task-switching Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Seminar presence — maintains active, attentive engagement during mathematical talks and colloquia, processing presented arguments in real time rather than passively attending 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.
  3. Stress response awareness — recognizes personal cognitive and emotional stress signals during high-stakes deadlines or conference presentations and applies intentional regulation strategies Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Applying
  1. Deliberate proof reading — reviews own and others' manuscripts with full present-moment attention, catching logical gaps and notational inconsistencies that distracted reading misses 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.
  2. Intentional collaboration presence — brings full attention to research discussions and co-working sessions, listening actively to collaborators' reasoning before formulating responses Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  3. High-stakes composure — delivers conference presentations and responds to expert audience challenges with calm, composed attention, even under adversarial or highly critical questioning Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Exceeding
  1. Contemplative research practice — cultivates a sustained, reflective relationship with mathematical problems, allowing incubation and non-linear insight development through disciplined mental spaciousness Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Mindful mentorship — attends fully to mentees' intellectual and professional development needs in each interaction, noticing unspoken confusion or discouragement and responding with calibrated support 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.
10Fortitude10 statements
Emerging
  1. Problem persistence — continues working on an assigned mathematical problem after initial approaches fail, making at least two or three distinct attempts before seeking assistance Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Criticism tolerance — receives and processes negative peer or instructor feedback on mathematical work without withdrawing from subsequent research engagement Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Developing
  1. Multi-month problem endurance — sustains productive effort on a single difficult mathematical problem across an extended period, managing discouragement and maintaining methodical progress 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.
  2. Rejection recovery — responds to manuscript rejection or conference paper decline by reassessing the work, strengthening the argument, and resubmitting within a defined timeframe Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  3. Uncertainty tolerance — continues advancing mathematical research in the absence of a clear solution path, operating productively at the frontier where outcomes are genuinely unknown 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.
Applying
  1. Major conjecture pursuit — dedicates substantial research effort to attacking a significant open problem in mathematics, sustaining engagement despite repeated setbacks over years 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.
  2. High-pressure deadline performance — produces rigorous, publication-quality mathematical work under grant, conference, or institutional deadlines without compromising standards Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  3. Adversarial peer review resilience — responds to hostile or deeply skeptical referee reports with equanimity, addressing every objection methodically and resubmitting with strengthened proofs Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Exceeding
  1. Decade-scale research courage — pursues a transformative but high-risk mathematical research program over a career arc, resisting pressure to shift to safer, more immediately publishable work 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.
  2. Community resilience modeling — demonstrates and articulates to junior mathematicians how sustained courage and persistence through failure are constitutive of mathematical achievement, shaping the professional culture of research groups 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.
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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Source anchors that ground each statement

Related titles
Agent-Based Modeler · Algebraist · Applied Mathematician · Cipher Expert · Computational Mathematician · Computational Scientist · Cryptanalyst · Cryptographer · Cryptographic Vulnerability Analyst · Engineering Mathematician · Game Mathematician · Geometrician
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.