Occupation · SOC 15-2021
Mathematicians
Conduct research in fundamental mathematics or in application of mathematical techniques to science, management, and other fields. Solve problems in various fields using mathematical methods.
Median wage
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Projected growth
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Annual openings
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per year
Employed (US)
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Job Zone 5
Typical preparation
Extensive preparation
Stackable credential programs
966 mapped
Core skills
MathematicsCritical ThinkingComplex Problem SolvingReading ComprehensionActive LearningScienceWritingJudgment and Decision MakingSpeakingLearning StrategiesActive ListeningSystems AnalysisSystems EvaluationInstructingMonitoringTime ManagementSocial PerceptivenessCoordinationPersuasionProgrammingOperations AnalysisManagement of Personnel ResourcesService OrientationNegotiationTechnology DesignOperations MonitoringManagement of Material ResourcesManagement of Financial ResourcesQuality Control AnalysisTroubleshootingRepairingOperation and ControlInstallationEquipment SelectionEquipment Maintenance
Knowledge areas
MathematicsEnglish LanguageComputers and ElectronicsEducation and TrainingEngineering and TechnologyPhysicsAdministration and ManagementForeign LanguageDesignCommunications and MediaBiologyCustomer and Personal ServiceChemistryEconomics and AccountingAdministrativePublic Safety and SecurityPersonnel and Human ResourcesLaw and GovernmentTelecommunicationsPsychologyMedicine and DentistrySales and MarketingTransportationMechanicalProduction and ProcessingSociology and AnthropologyPhilosophy and TheologyHistory and ArcheologyGeographyTherapy and CounselingFood ProductionFine ArtsBuilding and Construction
Technology & tools
AMPLARfitAdobe PhotoshopAlgaeAnalyse-itAnalysis and Visualization of Time Sequences AVTSApfloatApple ShazamApple macOSAptech Systems GAUSSAtlassian JIRAAztecBashCC#C++Cascading style sheets CSSComputer Algebra System for Algebraic Geometry CASADSP Development DADiSPData visualization softwareDataDescription DataDeskDifEquDiscrete Dynamics Lab DDLabEleSoft ResearchExtensible markup language XMLFormula translation/translator FORTRANGNU OctaveGeomviewGraphPad Software GraphPad PrismGraphics Programming Environment GRAPEHypertext markup language HTMLIBM SPSS AmosIBM SPSS StatisticsInsightful S-PLUSInteractive Mathematical Proof System IMPSJACALJavaScriptKANTKSEGLINDO Systems LINDO API
Representative tasks
Analyzing Data or InformationMaking Decisions and Solving ProblemsProcessing InformationWorking with ComputersUpdating and Using Relevant KnowledgeThinking CreativelyGetting InformationInterpreting the Meaning of Information for OthersCommunicating with Supervisors, Peers, or SubordinatesTraining and Teaching OthersCommunicating with People Outside the OrganizationIdentifying Objects, Actions, and EventsDeveloping Objectives and StrategiesProviding Consultation and Advice to OthersEstablishing and Maintaining Interpersonal RelationshipsDocumenting/Recording InformationCoaching and Developing OthersEstimating the Quantifiable Characteristics of Products, Events, or InformationOrganizing, Planning, and Prioritizing WorkCoordinating the Work and Activities of OthersEvaluating Information to Determine Compliance with StandardsJudging the Qualities of Objects, Services, or PeopleDeveloping and Building TeamsMonitoring Processes, Materials, or SurroundingsScheduling Work and ActivitiesGuiding, Directing, and Motivating SubordinatesPerforming Administrative ActivitiesStaffing Organizational UnitsResolving Conflicts and Negotiating with OthersMonitoring and Controlling ResourcesSelling or Influencing OthersPerforming for or Working Directly with the PublicAssisting and Caring for OthersInspecting Equipment, Structures, or MaterialsDrafting, Laying Out, and Specifying Technical Devices, Parts, and EquipmentControlling Machines and ProcessesHandling and Moving ObjectsRepairing and Maintaining Electronic EquipmentPerforming General Physical ActivitiesRepairing and Maintaining Mechanical Equipment
Competency framework
Skill expectations by proficiency level.
emerging
Mathematical notation and symbolic representations — apply to address relationships between quantities, magnitudes, and forms under faculty or senior mathematician guidance.Numerical analysis methods — execute standard computations on structured datasets within a supervised research or academic laboratory setting.Professional journals and conference proceedings — review regularly to build foundational awareness of current developments in assigned mathematical subdisciplines.Algebraic and geometric principles — investigate known relationships and reproduce established proofs under the direction of a research supervisor.Analytical or scientific software tools — operate to support assigned computational tasks within a university or government research environment.Sets of assumptions — assemble under supervision and enumerate immediate logical consequences for well-defined, bounded mathematical problems.Research findings — summarize in written draft reports following established conventions for internal review by a supervising mathematician.Undergraduate or early graduate students — assist in tutoring sessions on mathematical techniques under the oversight of a lead instructor.Object-oriented and development environment software — utilize to implement basic algorithms supporting mathematical research tasks.Literature in traditional areas such as probability and logic — read and synthesize to identify gaps relevant to an assigned research project.
developing
Computations and numerical analysis methods — perform independently on moderately complex datasets within applied research or industry analytical environments.Relationships between quantities and mathematical forms — explore and document using symbolic reasoning with routine oversight on multi-phase research projects.Research contributions — disseminate by drafting and submitting papers to peer-reviewed journals or presenting findings at professional conferences.Algebraic, geometric, and probabilistic frameworks — apply to extend established results in focused research problems with limited senior direction.Assumption sets for mathematical models — construct and systematically evaluate competing consequences in support of ongoing institutional research.Professional conferences and peer networks — engage with regularly to stay current and incorporate emerging techniques into daily research practice.Junior researchers or graduate students — mentor on core mathematical techniques and software tools within a laboratory or departmental setting.Analytical and scientific software platforms — configure and adapt to address non-standard computational problems arising in research workflows.Technical reports and research papers — write with clear argumentation and precise notation suitable for submission to domain-specific publications.Systems of mathematical relationships — analyze using deductive and inductive reasoning to validate model assumptions in applied or theoretical contexts.
proficient
New mathematical principles and inter-domain relationships — develop autonomously to advance knowledge in areas such as algebra, topology, or stochastic analysis.Complex, non-routine mathematical problems — solve across the full research lifecycle from problem formulation through proof or computational verification.Research dissemination strategy — execute by publishing in high-impact journals, delivering invited conference presentations, and contributing to edited volumes.Comprehensive assumption sets for novel models — assemble and rigorously explore all consequence branches, identifying theoretical boundaries and failure modes.Numerical analysis and advanced computational methods — apply at scale to large, ambiguous datasets within cross-disciplinary research or industrial R&D environments.Graduate students and early-career mathematicians — mentor on specialized mathematical techniques, proof strategies, and professional research practice.Emerging literature across mathematics, physics, and computer science — critically synthesize to identify convergences that open new research directions.Analytical software, scientific computing platforms, and programming environments — integrate to build reproducible, high-performance mathematical research pipelines.Oral and written communication of advanced mathematical results — tailor for diverse audiences ranging from specialist peers to interdisciplinary collaborators.Evaluation of mathematical systems and models — conduct using systems analysis and monitoring methods to assess correctness, scalability, and applicability.
advanced
Field-level research agenda — define and champion across institutional, funding, and international scholarly communities to shape the trajectory of a mathematical discipline.Novel theoretical frameworks connecting previously unrelated mathematical domains — originate and validate, producing results with broad scientific impact.Doctoral researchers and postdoctoral fellows — develop through sustained mentorship, personalized learning strategies, and integration into high-visibility research programs.Institutional research programs — lead by securing major grants, forming cross-sector partnerships, and aligning mathematical inquiry with national or global priorities.Peer-reviewed publications, monographs, and keynote addresses — produce at an authoritative level that establishes citation-defining contributions to mathematical science.Complex assumption-driven models addressing high-stakes real-world problems — architect and oversee from theoretical design through computational deployment in government or industry.Cross-disciplinary collaboration frameworks — establish between mathematics departments and fields such as physics, computer science, and engineering to accelerate applied innovation.Organizational knowledge-management systems and research workflows — design and evaluate to maximize productivity and reproducibility across large mathematical research teams.Standards and best practices for mathematical education and training — develop and promulgate at curriculum, departmental, or national professional-society levels.Strategic technology adoption — guide at the organizational level by evaluating emerging analytical platforms and development environments for alignment with long-term research objectives.
Also known as
17 alternate job titles map to this occupation.
Agent-Based ModelerAlgebraistApplied MathematicianCipher ExpertComputational MathematicianComputational ScientistCryptanalystCryptographerCryptographic Vulnerability AnalystEngineering MathematicianGame MathematicianGeometricianMath Researcher (Mathematics Researcher)MathematicianResearch Computing SpecialistResearch ScientistResearcher