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SOC 15-2041 · O*NET 15-2041.00
This page uses the BLS Occupational Outlook Handbook's combined scope for mathematicians and statisticians. Mathematicians (O*NET 15-2021.00) research fundamental mathematics or applications of mathematical techniques to science, management, and other fields. Statisticians (O*NET 15-2041.00) develop or apply mathematical and statistical theories and methods to collect, organize, interpret, and summarize numerical data into useful information.
Model impact index for three equally weighted representative core tasks; not a measured share of working time or a job-loss probability. floor((75+75+50)/3+0.5)=67; fermatmind-ai-impact-v1; 2026-10-18.
Mathematicians and statisticians, in the combined scope, focus on analyzing data and solving problems with computational methods. One side researches fundamental mathematics or applications of mathematical techniques to science, management, and other fields, develops new relationships among mathematical principles, formulates hypotheses and derives consequences, and conducts numerical analysis and modeling. The other develops or applies statistical theory and methods, designs and evaluates experiments and sampling, prepares and organizes raw data, analyzes and interprets significant differences, judges statistical method applicability, presents results through charts and papers, and adapts statistical methods to problems in economics, biology, engineering, and other fields.
The following assessments concern research and analysis by mathematicians and statisticians (BLS combined scope). They do not predict hiring, qualifications, authorization, or research results.
Sample output and reflection: Check whether you first defined the problem and assumptions, explained methods and applicability conditions, provided verifiable conclusions and limitations, and distinguished proof from statistical approximation. Then ask whether you can sustain derivation and analysis, honestly acknowledge uncertainty when data are insufficient, and take responsibility for conclusions and citation standards.
This page uses the BLS Occupational Outlook Handbook's combined scope for mathematicians and statisticians, including O*NET 15-2021.00 Mathematicians and 15-2041.00 Statisticians, with directions such as computational mathematics, cryptography research, statistical analysis, and biostatistics. Work includes fundamental mathematics research and mathematical applications across fields, or designing and evaluating statistical methods and sampling, preparing and organizing data, analyzing and interpreting data, judging method applicability, presenting results through charts and papers, developing modeling and graphical analysis programs, and guiding data collectors. Work is mainly in offices and computing environments; major employers are government and R&D institutions. This page excludes adjacent roles such as financial quantitative analysts, computer and information research scientists, and operations research analysts. Statisticians are a constituent occupation of this combined group, and biostatistics is a statistical specialty; neither should be listed as excluded from the group.
Career direction comparison
The following compares mathematicians and statisticians and adjacent roles by actual objects of work, core deliverables, and method boundaries. Qualifications are not interchangeable based on titles.
| Career direction | Core work and output | Key differences | Best-fit choice |
|---|---|---|---|
| Financial Quantitative Analysts | Financial quantitative analysts focus on financial market modeling and trading strategies; mathematicians and statisticians focus on research and applications of mathematical theory and statistical methods, with different objectives and deliverables. | Focus on financial modeling and trading strategies. | Compare if you prefer financial quantitative work. |
| Computer and Information Research Scientists | Computer and information research scientists focus on frontier computing and information science research; mathematicians and statisticians focus on mathematical and statistical methods, with different emphases. |
AI impact on this career
Tools for symbolic computation and theorem-proving assistance, statistical modeling and automated analysis, data organization and visualization, and report and paper drafting can assist calculation verification, model exploration, and material organization. Researchers remain responsible for problem definition, assumption selection, method applicability judgments, conclusion reliability, and academic standards. Tools must not replace rigorous reasoning and review. AI Impact Score 67% is an editorial estimate. Model impact index for three equally weighted representative core tasks; not a measured share of working time or a job-loss probability. floor((75+75+50)/3+0.5)=67; fermatmind-ai-impact-v1; 2026-10-18.The three tasks, ratings and sources are listed in the FermatMind method source record on this page.
FermatMind AI Impact Score estimation method v1
FermatMind / 费马测试 · 2026-10-18
Editorial ratings use the existing occupational responsibilities and AI task analysis on this page. They are not adoption rates, measured effects, job-disappearance or personal-unemployment probabilities, or official scores from Stanford or another external institution. No measured time weights or future robot deployment are assumed.
Chinese mainland salary reference
Scope note: National Bureau of Statistics 2025 average annual wages for persons employed in scientific research and technical services were RMB 182,064 per year in urban non-private units and RMB 83,560 per year in urban private units; the national total for urban non-private units was RMB 129,441 per year. All are industry-level figures, not this occupation's median or starting pay.
Category boundaries: Ministry of Human Resources and Social Security enterprise compensation survey information is classified by occupation and position and can be used to look up research and data-related pay. This page did not obtain an entry precisely corresponding to O*NET 15-2021.00 or 15-2041.00 and does not use it as this occupation's national median. Refer to releases from responsible authorities.
Only average annual wages are published
U.S. salary reference
The BLS Occupational Outlook Handbook page displays a 2025 combined median annual wage of $105,720 (about $50.83 per hour), with separate medians of $126,710 per year for mathematicians and $105,650 for statisticians (May 2025). Combined employment was about 33,500 in 2025, with projected 10% growth in 2025–2035 (much faster than average), employment change of about +3,400, and about 2,000 average annual openings. The page provides no combined-group percentiles, but its Pay section provides separate mathematician and statistician percentiles; these cannot be averaged or reused as combined percentiles. These are U.S. national combined figures, not precise values for either constituent occupation or individual employment outcomes.
| Percentile | Annual reference | Hourly equivalent | Explanation |
|---|---|---|---|
| 10th percentile (combined) | Insufficient evidence: Combined percentiles not obtained |
Fit signals
To assess fit, consider whether you can sustain abstract derivation or data analysis, rigorously design and evaluate methods, honestly acknowledge insufficient data, present conclusions in charts and writing, and continue reading literature and writing. Tools such as RIASEC only generate hypotheses and cannot replace real task experience.
Positive signals： Positive signals: Abstract thinking or systematic data analysis, rigorous verification, honesty about uncertainty, clear presentation of results, and sustained learning and writing.
Reasons for caution： Reasons for caution: Difficulty sustaining derivation or data analysis, a tendency to skip verification or overstate conclusions, unwillingness to write and undergo review, or difficulty handling competition and sustained output pressure.
Trial action： Trial action: With an entirely fictional research or data problem, practice method selection, an analysis or proof approach, and verification methods, then ask someone to review them against your records.
Risks and boundaries
Address risks through triggers, consequences, controls, and escalation boundaries.
Editorial risk analysis: O*NET statistical tasks inform method, data, and inference control points; mathematician work context describes pressure for that constituent only; BLS explains combined statistical boundaries. Check citations and academic standards with institutions. This is not evidence of statutory liability or incident rates.
Typical scenario：Insufficient conditions for assumptions or method applicability.
Roles most affected：Research and analysis positions
Possible consequence：May affect whether conclusions hold.
How to reduce risk：Check assumptions and applicability conditions and review.
Entry pathways
In the U.S., this occupation is in Job Zone 5 (extensive preparation needed). BLS OOH states that a mathematics or statistics master's degree is typically required at minimum, with some positions accepting bachelor's degrees. O*NET statistician respondents report about 62% master's degrees, 14% bachelor's degrees, and 10% doctorates. Check specific requirements with employers.
Market signals
BLS Occupational Outlook Handbook reports combined mathematician and statistician employment of about 33,500 in 2025, projected 10% growth in 2025–2035 (much faster than average), employment change of about +3,400, and about 2,000 average annual openings. These are combined occupational statistics, not an individual's hiring probability or a sample of job postings.
U.S. national · Display scope: Mathematicians and Statisticians (combined scope)
U.S. combined employment was 33,500 in 2025, with projected 10% growth in 2025–2035, net growth of about 3,400, and about 2,000 average annual openings. This is an overall employment projection, not attributed to AI.
Employment size and change
The overall employment projection is not attributed to AI; size, net growth, and average annual openings are not interchangeable.
Does not establish：Combined statistics cannot serve as individual employment guarantees.
This page uses the BLS Occupational Outlook Handbook's combined scope for mathematicians and statisticians. Mathematicians (O*NET 15-2021.00) research fundamental mathematics or applications of mathematical techniques to science, management, and other fields. Statisticians (O*NET 15-2041.00) develop or apply mathematical and statistical theories and methods to collect, organize, interpret, and summarize numerical data into useful information. Work includes mathematical research and applications, or designing and evaluating statistical methods and sampling, organizing and analyzing data, judging method applicability, presenting results in charts and papers, and guiding data collection. Work is mainly in offices and computing environments. This is distinct from financial quantitative analysts, computer and information research scientists, operations research analysts, statisticians, or biostatisticians.
Choose a real task from this page for a small practice project or a conversation with someone in the field. Use the planning guides to set a date, an output and feedback questions before deciding whether to continue.
This is an entirely fictional research or data analysis scenario check, not a personality diagnosis, hiring conclusion, or qualification assessment.
Entirely fictional task package: Provide a fictional research or data problem, including 1 problem and objective statement, 1 set of sample or simulated data, and 1 hypothesis to model or test. Within 60 minutes, write method selection and assumptions, an analysis or proof approach, verification methods and limitations, and explain how results can be tested. Do not use real confidential data or others' unpublished findings.
Check first: Problems and assumptions, research and sampling designs, data sources and definitions, method and model applicability conditions, error and verification requirements, and academic standards and funding boundaries.
Work cycle: Define problems and assumptions, design research or select methods, organize and analyze data, model or prove, verify results, present findings, and undergo review. Do not draw conclusions before confirming all data definitions and method applicability conditions, or submit for publication before checking citations and output boundaries.
| Dimension | Primary track | Comparison track |
|---|---|---|
| Complete cycle | From defining problems to undergoing review | |
| Step one | Define problems and assumptions | |
| Step two | Design research or select methods | |
| Step three | Collect and organize data | |
| Step four | Analyze, model, or prove | |
| Step five |
Work inputs: Mathematical or statistical problems and hypotheses, observational or sample data, experimental and sampling designs, computational and statistical methods, modeling needs and application contexts, literature and existing findings, and funding and collaboration information.
Verifiable outputs: Proofs and theorems, statistical inferences and conclusions, models and algorithms, data analyses and charts, research reports and papers, method evaluations and applicability explanations, and recommendations for applied problems.
Complete workflow: Define the problem and assumptions → design research and sampling or select methods → collect and organize data → analyze, model, or prove → verify results and limitations → present findings and undergo review to complete the cycle.
In the U.S., a mathematics or statistics master's degree is typically required at minimum, with some positions accepting bachelor's degrees; O*NET statistician feedback reports about 62% master's degrees. No practice license is universally required. Check title and project reviews with institutions.
AI boundaries for mathematicians and statisticians Tools for symbolic computation and theorem-proving assistance, statistical modeling and automated analysis, data organization and visualization, and report and paper drafting can assist calculation verification, model exploration, and material organization. Researchers remain responsible for problem definition, assumption selection, method applicability judgments, conclusion reliability, and academic standards. Tools must not replace rigorous reasoning and review.
| Focus on frontier computing and information research. |
| Compare if you prefer computing research. |
| Operations Research Analysts | Operations research analysts focus on resource and decision optimization; mathematicians and statisticians focus on mathematical theory, statistical inference, and applications, with broader sources of problems. | Focus on resource and decision optimization. | Compare if you prefer optimization applications. |
|---|
| Statisticians | Statisticians and biostatisticians are more precise occupations in the statistical direction. This page uses a combined scope; conclusions about statistics alone or biomedical statistics should follow the corresponding precise occupation. | A more precise occupational scope in statistics. | Compare if you prefer statistical inference. |
|---|
First use a verifiable research or analysis explanation to check assumptions, method applicability, and conclusion boundaries, then assess a direction. Do not assign a single ranking based on income or personality.
Next, turn the comparison into a small-scale research or analysis exercise that can be stopped.
Describe only specific steps tools can assist with; do not treat demonstrations as institutional adoption.
Insufficient evidence: Adoption rates and job outcomes for the combined mathematician and statistician group were not obtained. Check data, tools, and human review responsibility before trials.
Without occupational-level job outcome research, do not infer layoff timing, staffing changes, or hiring probabilities.
| Work area | Task | Current change | Human control point |
|---|---|---|---|
| Modeling and analysis | Build models and analyze data | Editorial recommendation: Tools may assist data organization, statistical modeling, and document drafting. Current materials do not demonstrate widespread institutional adoption of these systems. | Check data and assumptions. |
| Presentation and reporting | Present results and write reports | May assist drafting | Follow assumptions, method applicability, and academic standards, retaining human judgment and records. |
| Methods and verification | Assess methods and verify conclusions | No automated decisions | Confirmed by the researcher. |
| Standards and review | Follow standards and undergo review | Cannot replace judgments involving responsibility | Confirmed by the researcher and reviewers. |
Occupational sources describe actual tasks and objects of work: problems and assumptions, data and designs, models and proofs, and reports and findings. Tool capabilities, institutional adoption, and job outcomes are recorded separately. Wage or employment data are not substitutes for AI evidence.
Editorial recommendation: Try data organization, model exploration, and document drafting, evaluating accuracy and review costs separately. Task and exposure materials cannot establish adoption priority or the relative strength of employment impacts.
AI primarily changesEditorial recommendation: Try data analysis and modeling assistance
Human responsibility remainsAssumption and method judgments
AI primarily changesEditorial recommendation: Try document drafting assistance
Human responsibility remainsConclusions and responsibility
Human control points: Define problems and assumptions, design and evaluate research methods, judge model applicability and errors, take responsibility for conclusions and citation standards, and follow academic ethics and funding agreements.
Confirm problems, data, and standards.
Analyze only within academic and ethical boundaries.
Review methods, calculations, and conclusions.
Promptly report standards and ethical issues.
May affect whether conclusions hold.
Control: Check applicability conditions and review.
May lead to misleading conclusions.
Control: Check sources and definitions.
May violate academic integrity.
Control: Follow standards and check citations.
Practice modeling, analysis, and writing.
Retain method and data records.
Set standards and review requirements first.
Task exposure, adoption, and job outcomes measure different things and cannot establish a date for job cuts.
Source: O*NET 15-2041.00 Statisticians TasksOriginal source ↗
Currently, only assistable data analysis, modeling, and document drafting are described. Humans retain responsibility for assumption selection, method judgments, and conclusions.
Source: O*NET 15-2041.00 Statisticians TasksOriginal source ↗
There is no occupational-level adoption-rate source, so this page does not provide such figures.
Source: BLS Occupational Outlook Handbook: Mathematicians and Statisticians (combined scope)Original source ↗
First conduct an offline exercise with an entirely fictional research or data problem. Write method selection, an analysis or proof approach, and verification methods without relying on unverified automated analysis to replace rigorous judgment.
Only average annual wages are published
Insufficient evidence: Not separately listed
This page did not obtain a national median wage for this combined group in mainland China. The figures below are industry average annual wages in urban units, not starting pay, a combined median, or take-home income.
| Role scope | Reference value | Explanation |
|---|---|---|
| Not separately reported | Appointment by employer and position | National Bureau of Statistics wage data are classified by industry and registration type, not education levels for this occupation. |
| Not separately reported | Appointment by employer and position | National Bureau of Statistics wage data are classified by industry and registration type, not education levels for this occupation. |
| Not separately reported | Appointment by employer and position | National Bureau of Statistics wage data are classified by industry and registration type, not education levels for this occupation. |
| Not separately reported | Appointment by employer and position | National Bureau of Statistics wage data are classified by industry and registration type, not education levels for this occupation. |
RMB 182,064 per year
RMB 83,560 per year
RMB 129,441 per year
Insufficient evidence: A national occupational median wage, statistical period, and definition for mathematicians and statisticians in mainland China were not obtained. This page displays only labeled industry proxies and does not fill gaps with proxy or U.S. numbers.
| — |
| The same BLS page separately lists constituent-occupation percentiles. They cannot be calculated or averaged into combined-group percentiles and do not indicate seniority. |
| Median (50%) | $105,720 per year (combined) | $50.83 per hour | 2025 U.S. national combined median annual wage (mathematicians and statisticians combined scope). |
|---|
| 90th percentile (combined) | Insufficient evidence: Combined percentiles not obtained | — | The same BLS page separately lists constituent-occupation percentiles. They cannot be calculated or averaged into combined-group percentiles and do not indicate seniority. |
|---|
Pay · Median：$105,720 per year (2025, combined scope)；BLS OOH: Mathematicians and Statisticians (Pay, 2025 combined scope)
Pay · Hourly median：$50.83 per hour (2025, combined scope)；BLS OOH: Mathematicians and Statisticians (Pay, 2025 combined scope)
Pay · 10th percentile (combined)：Insufficient evidence: Combined percentiles not obtained；BLS OOH: Mathematicians and Statisticians (Pay, 2025 combined scope)
Pay · 90th percentile (combined)：Insufficient evidence: Combined percentiles not obtained；BLS OOH: Mathematicians and Statisticians (Pay, 2025 combined scope)
Pay · Statistical scope：Mathematicians and Statisticians (combined scope)；BLS OOH: Mathematicians and Statisticians (Pay, 2025 combined scope)
2025 combined median of $105,720 per year; constituent medians are $126,710 for mathematicians and $105,650 for statisticians. Separate percentiles appear on the same page; combined-group percentiles were not obtained.
Combined employment size in 2025, not job postings.
Projected combined growth of 10% in 2025–2035 (much faster than average) is an occupational statistic, not an individual's hiring outcome.
Major employers are the federal government and scientific research and development institutions; this does not represent all practitioners' income.
| Industry | 2025 constituent occupation × industry median | How to interpret |
|---|---|---|
| Mathematicians | Federal government | $136,990 per year (2025) | BLS OOH Pay constituent occupation × industry median reference; not a combined-group industry median. Do not combine these into a range for this group. |
| Mathematicians | State colleges, universities, and professional schools | $65,510 per year (2025) | BLS OOH Pay constituent occupation × industry median reference; not a combined-group industry median. Do not combine these into a range for this group. |
| Statisticians | Federal government | $132,620 per year (2025) | BLS OOH Pay constituent occupation × industry median reference; not a combined-group industry median. Do not combine these into a range for this group. |
| Statisticians | Research and development in the physical, engineering, and life sciences | $130,590 per year (2025) | BLS OOH Pay constituent occupation × industry median reference; not a combined-group industry median. Do not combine these into a range for this group. |
BLS indicates a master's is typical, with some positions accepting bachelor's degrees. Check appointments, titles, and specific authority by jurisdiction and institution; directories cannot prove the absence of licensing requirements.
Editorial recommendation: Show research, methodological, and data analysis outputs. Current occupational materials do not support comparisons of the relative hiring validity of outputs and certificates.
Strongly affected by the distribution of government and R&D institutions; do not extrapolate across regions.
BLS OOH: Mathematicians and Statisticians (Job Outlook, 2025–2035 combined scope)
BLS OOH: Mathematicians and Statisticians (Job Outlook, 2025–2035 combined scope)
BLS OOH: Mathematicians and Statisticians (Job Outlook, 2025–2035 combined scope)
O*NET occupational interest baseline
Do not choose a career based on a single code.First observe interest, stress, and experience in actual derivation and proof, data analysis, and writing and presentations.
Activity preferences can only help design exercises; they cannot determine qualifications or performance.
Check through work samples rather than substituting labels for judgment.
The O*NET interest code is IC (Investigative–Conventional): an inclination toward research and analysis and organizing symbolic and data information according to procedures. These labels describe activity preferences only and cannot determine competence or qualifications.
Do not use it this way: Hiring, qualifications, or performance cannot be inferred from this.
Start a career interest exerciseCheck through work samples rather than substituting labels for judgment.
General personality measures such as the Big Five provide no job-specific evidence for this occupation and support self-reflection only. Continue checking through actual derivation and proof, data analysis, and writing and presentation experience.
Do not use it this way: Hiring, qualifications, or performance cannot be inferred from this.
Start a career interest exerciseCheck through work samples rather than substituting labels for judgment.
Type tools such as MBTI and the Enneagram cannot determine competence or qualifications and support self-reflection only.
Do not use it this way: Hiring, qualifications, or performance cannot be inferred from this.
Start a career interest exerciseCheck through work samples rather than substituting labels for judgment.
Continue checking against actual tasks, boundaries, and verifiable deliverables.
Do not use it this way: Hiring, qualifications, or performance cannot be inferred from this.
Start a career interest exerciseCheck through work samples rather than substituting labels for judgment.
Continue checking against actual tasks, boundaries, and verifiable deliverables.
Do not use it this way: Hiring, qualifications, or performance cannot be inferred from this.
Start a career interest exerciseCheck through work samples rather than substituting labels for judgment.
Continue checking against actual tasks, boundaries, and verifiable deliverables.
Do not use it this way: Hiring, qualifications, or performance cannot be inferred from this.
Start a career interest exerciseFits better when: Can design research and develop hypotheses.
Watch for: Must check methods and sampling.
Fits better when: Can organize and validate data.
Watch for: Must check definitions and sources.
Fits better when: Can model and make inferences.
Watch for: Must check applicability conditions.
Fits better when: Can perform numerical and programmed computation.
Watch for: Must check errors and implementation.
Fits better when: Can present through charts and papers.
Watch for: Must check standards and citations.
Fits better when: Can apply methods to cross-disciplinary problems.
Watch for: Must check application context.
Use this page's work sample to check research design.
Check definitions and assumptions against the method.
Assess methodological judgment.
Check first and indicate uncertainty.
Assess charting and writing skills.
Assess responsibility and academic ethics awareness.
Enable others to review it through method and conclusion records.
Complete an exercise with an entirely fictional research or data problem.
Evidence：O*NET 15-2041.00 Statisticians Tasks
Typical scenario：Unreliable data sources or definitions.
Roles most affected：Data and analysis positions
Possible consequence：May lead to misleading conclusions.
How to reduce risk：Check sources and definitions.
Evidence：O*NET 15-2041.00 Statisticians Tasks
Typical scenario：Insufficiently rigorous conclusions or inferences.
Roles most affected：Research positions
Possible consequence：May lead to incorrect conclusions.
How to reduce risk：Verify rigorously and undergo review.
Evidence：O*NET 15-2041.00 Statisticians Tasks
Typical scenario：Citations or findings fail to meet academic standards.
Roles most affected：Research and publication positions
Possible consequence：May violate academic integrity.
How to reduce risk：Follow standards and check citations.
Evidence：BLS Occupational Outlook Handbook: Mathematicians and Statisticians (combined scope)
Typical scenario：Competition and sustained output pressure.
Roles most affected：Research positions
Possible consequence：May affect career stability and health.
How to reduce risk：Manage pace and seek collaboration.
Evidence：O*NET 15-2021.00 Work Context
Typical scenario：Using combined statistics as precise single-occupation values.
Roles most affected：Research and analysis positions
Possible consequence：May produce scope errors.
How to reduce risk：Check combined scope and distinguish single-occupation values.
Evidence：BLS Occupational Outlook Handbook: Mathematicians and Statisticians (combined scope)
Typical scope：Entry stage: Under supervision, practice literature reading and problem definition, statistical and numerical methods, data organization and analysis, programming and visualization, academic writing, and presentations. Learn academic standards and retain process records.
Readiness evidence：Evidence to show: Use a verifiable research or analysis explanation, including problem and assumptions, methods and data, conclusions and limitations, to demonstrate rigorous reasoning and honest documentation.
Credential boundary：Verify education and project requirements.
Next moves：Next step: Check the target institution's research or business direction and requirements, data and compliance constraints, and findings and citation standards. Verify modeling, analysis, and writing skills in supervised real research or analysis.
Typical scope：Conduct independent research or analysis and undergo review.
Readiness evidence：Retain method and findings records.
Credential boundary：Verify institutional and title requirements.
Next moves：Progression to greater responsibility: With experience, lead independent projects or analysis directions, mentor and collaborate in teams, develop a specialty, or move into data science, quantitative analysis, or teaching.
Typical scope：Lead directions and projects.
Readiness evidence：Retain direction and project records.
Credential boundary：Verify title requirements.
Next moves：Build project and mentoring evidence.
Typical scope：Lead teams and funding.
Readiness evidence：Retain team and funding records.
Credential boundary：Verify institutional requirements.
Next moves：Build governance and strategy evidence.
Typical scope：Participate in data analysis under supervision.
Readiness evidence：Retain analysis records.
Credential boundary：Verify employer requirements.
Next moves：Build data and modeling foundations.
Typical scope：Independently handle modeling and analysis.
Readiness evidence：Retain model and analysis records.
Credential boundary：Verify employer requirements.
Next moves：Build engineering and business evidence.
Typical scope：Lead complex models and solutions.
Readiness evidence：Retain complex model records.
Credential boundary：Verify employer requirements.
Next moves：Build evidence of methodological systems.
Typical scope：Lead teams and methodological standards.
Readiness evidence：Retain team and standards records.
Credential boundary：Verify employer requirements.
Next moves：Build evidence of management responsibility.
Typical scope：Participate in teaching or applied analysis under supervision.
Readiness evidence：Retain teaching and application records.
Credential boundary：Verify institutional and employer requirements.
Next moves：Build teaching or application foundations.
Typical scope：Independently handle courses or application tasks.
Readiness evidence：Retain course and application records.
Credential boundary：Verify institutional and employer requirements.
Next moves：Build results and evidence.
Typical scope：Lead curricula or application projects.
Readiness evidence：Retain system and project records.
Credential boundary：Verify title and employer requirements.
Next moves：Build governance and impact evidence.
Typical scope：Lead a discipline or direction and team.
Readiness evidence：Retain discipline and team records.
Credential boundary：Verify title and employer requirements.
Next moves：Build strategy and governance evidence.
Confirm problems, data, and standards.
Design, analyze, and verify according to methods.
Create verifiable method and findings records.
Expand project and application responsibilities within authorization.
U.S. national · Display scope: Mathematicians and Statisticians (combined scope)
About 2,000 per year
Job openings (annual average)
Average over the 2025–2035 decade, including growth and replacement needs, not current job vacancies.
Does not establish：Cannot serve as an individual's hiring probability.
U.S. national · Display scope: Mathematicians and Statisticians (combined scope)
$105,720 per year
Median annual wage
BLS 2025 combined median, not starting pay or take-home income.
Does not establish：Percentiles not disclosed; excludes individual take-home income.
These are capability relationships, not automatic promotions or credential waivers.
Transfers：Transferable capabilities: Mathematical and statistical modeling, data organization and analysis, programming and visualization, research methods and experimental design, academic writing and presentation, cross-disciplinary applications, and collaboration.
Build next：Gaps to address: Applied knowledge and programming skills in the target field, machine learning and data engineering methods, or experience and evidence of responsibility needed for operations optimization, data science, or quantitative analysis.
View career profileTransfers：Mathematics and computation foundations.
Build next：Build computing and information research expertise.
View career profileTransfers：Modeling and optimization foundations.
Build next：Build operations research and decision methods.
View career profileTransfers：Statistical inference and data methods.
Build next：Statisticians are a constituent occupation of the combined group. This card represents choosing a statistical-method focus, requiring specific task and employer evidence, rather than moving to an entirely new occupation.
View career profileTransfers：Statistics and biomedical foundations.
Build next：Biostatistics is a statistical specialty. Build biomedical research design, trial ethics, and domain data knowledge; check authority with the specific institution.
View career profileTransfers：Mathematics and modeling foundations.
Build next：Build data engineering and business experience.
View career profileFinancial quantitative analysts focus on financial modeling and trading; computer and information research scientists on computing and information research; operations research analysts on optimization. Statisticians and biostatisticians are more precise statistical occupations. This page uses a combined scope; compare objects, methods, and precise occupational definitions to distinguish them.
Observable signals: Abstract thinking or systematic data analysis, rigorous verification, honesty about uncertainty, clear presentation of results, and sustained learning and writing. The O*NET interest code IC describes activity preferences only and cannot determine competence or qualifications.
Tools for symbolic computation and theorem-proving assistance, statistical modeling and automated analysis, data organization and visualization, and report and paper drafting can assist calculation verification, model exploration, and material organization. Researchers remain responsible for problem definition, assumption selection, method applicability judgments, conclusion reliability, and academic standards. Tools must not replace rigorous reasoning and review. This page presents tool uses only as task hypotheses, not evidence of widespread institutional adoption.
Human responsibilities include defining problems and assumptions, designing and evaluating research methods, judging model applicability and errors, taking responsibility for conclusions and citation standards, and following academic ethics and funding agreements.
The National Bureau of Statistics publishes average annual wages for persons employed in urban units by broad industry category, without separately listing this combined scope, so a safely mapped national occupational median cannot be established. The page displays only labeled industry proxies: in 2025, scientific research and technical services recorded RMB 182,064 per year in urban non-private units and RMB 83,560 per year in urban private units; the national total for urban non-private units was RMB 129,441 per year. None equals this occupation's median or starting pay. Ministry of Human Resources and Social Security enterprise compensation survey information is a lookup resource.
The BLS Occupational Outlook Handbook page displays a 2025 combined median annual wage of $105,720 (about $50.83 per hour), with separate medians of $126,710 per year for mathematicians and $105,650 for statisticians (May 2025). That page does not display percentile wages. These are U.S. national combined figures, not individual take-home income or starting pay, and do not replace precise values for a single occupation.
In the U.S., a mathematics or statistics master's degree is typically required at minimum, with some positions accepting bachelor's degrees. O*NET statistician feedback reports about 62% master's, 14% bachelor's, and 10% doctoral degrees. No practice license is universally required. In mainland China, there is no uniform occupational qualification precisely corresponding to this O*NET occupation; check employer and industry requirements.
Main risks involve assumption and method applicability, data sources and definitions, conclusion and inference reliability, academic standards and citations, and competition and output pressure. Controls include checking assumptions and applicability conditions, clarifying data definitions, rigorous verification and uncertainty labeling, following academic standards, and managing output pace. Check specific rules with institutions and applicable standards.
BLS Occupational Outlook Handbook reports combined employment of about 33,500 in 2025, projected 10% growth in 2025–2035 (much faster than average), employment change of about +3,400, and about 2,000 average annual openings. These are combined occupational statistics, not an individual's hiring probability.
If you can sustain abstract derivation or data analysis and verify rigorously, try a low-cost exercise with an entirely fictional research or data problem. Moving into data science, operations optimization, or quantitative analysis requires applied expertise and experience evidence.
Evidence for China, the U.S., and specific institutions is presented separately: conclusions about pay, employment, qualifications or credentials, safety, and AI must not be combined across scopes. U.S. statistics on this page combine mathematicians and statisticians and do not replace precise single-occupation values.; The mathematicians and statisticians page provides occupational assessment and research practice information and does not replace local laws, academic standards, ethical requirements, or other professional advice.; 'Insufficient evidence' means only that safely corresponding data were not established through a bounded search; proxy data or memory are not used to fabricate numbers.
FermatMind research workflow
2025 median wages and 2025–2035 outlook; accessed 2026-09-25
BLS Occupational Outlook Handbook: Mathematicians and Statisticians (combined scope)
Limitations：Used only for 15-2021.00 and the U.S. market; does not establish a mapping to China.
Limitations：The task sample does not mean every position performs every task; it does not establish a mapping to China.
Limitations：Used only for 15-2041.00 and the U.S. market; does not establish a mapping to China.
Limitations：The task sample does not mean every position performs every task; it does not establish a mapping to China.
Limitations：U.S. work context does not replace Chinese law or employer procedures.
Limitations：Combined scope for mathematicians and statisticians, not precise single-occupation values; does not automatically map to other jurisdictions.
Limitations：Combined wage scope, not precise single-occupation values; does not automatically map to other jurisdictions.
Limitations：Combined employment and outlook scope, not precise single-occupation values; does not provide individual hiring probabilities.
Limitations：Industry distribution signals employer settings, not projected growth or demand.
Limitations：The education distribution does not constitute mandatory requirements for every employer; it does not establish a mapping to China.
Limitations：Certification and training do not equal a scope of practice or employment; check the applicable jurisdiction.
Limitations：Task exposure does not equal implemented automation, adoption rates, or layoffs; individual outcomes are not inferred.
Limitations：An industry average is not an occupational median and excludes individual businesses and freelancers; no national wage distribution precisely corresponding to this occupation was established.
Limitations：Covers urban enterprises, excluding government agencies and public institutions; this page did not obtain a precise single-occupation entry and does not use it as a national median.
Limitations：This editorial scale is not evidence of adoption rates, layoffs, regulations, or licensing.
Limitations：Editorial ratings use the existing occupational responsibilities and AI task analysis on this page. They are not adoption rates, measured effects, job-disappearance or personal-unemployment probabilities, or official scores from Stanford or another external institution. No measured time weights or future robot deployment are assumed.
BLS combined-group 2025 wages and 2025–2035 outlook have been checked. Pay separately lists constituent-occupation percentiles and industry wages; combined-group percentiles were not obtained. O*NET separately supports tasks and contexts for the two constituent occupations; mathematician working hours cannot represent the combined distribution. NBS provides industry-average references only, and ILO exposure background only. Protected older statements in the shared registry and FAQ, such as 'percentiles not displayed,' still conflict; no claim of whole-page consistency is made.
| Verify results and limitations |
| Step six | Present findings and undergo review |
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