What it pays
Government survey numbers — not estimates, not ads.
Half of all Mathematicians in the U.S. earn more than $126,710 a year — the middle 80% land between $69,240 and $195,190. About 2,030 people in the U.S. do this work. Figures are for the U.S. occupation group “Mathematicians”. (U.S. Bureau of Labor Statistics survey, published 2025.) In India, Professionals earn about ₹38,298 a month on average — around ₹4.6 lakh a year (government PLFS survey via ILOSTAT, occupation-family figure).
$126,710typical pay / year
2,030people in this work
$195,190+top 10% earn
₹4.6 lakha year in India (family avg)
Think you get this job?Six quick questions on how it really works — with a hint and the reason behind every answer.
Test yourself →The work, task by task
These are the real jobs-to-be-done, not a wish list. Each task shows where we found it, and the prompt underneath is written for that exact task.
Fixing1
Perform actuarial computations
+Run the life‑table and loss‑distribution calculations for the pension portfolio, update mortality and lapse…
Perform actuarial computations
+Run the life‑table and loss‑distribution calculations for the pension portfolio, update mortality and lapse parameters from last quarter's claims, produce the present‑value reserve table by cohort, and flag any lines where reserve increases exceed 5%.
The tools that do the workC++job descriptionsO*NETWikipedia
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Learning1
Mentor others on mathematical techniques
+Hold a two‑hour mentoring session with Ana and Marco to review measure theory heuristics, walk through three…
Mentor others on mathematical techniques
+Hold a two‑hour mentoring session with Ana and Marco to review measure theory heuristics, walk through three worked proofs on stochastic processes, assign targeted exercises based on their gaps, and schedule follow‑up in two weeks.
The tools that do the workLinuxjob descriptionsO*NETWikipedia
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Analysing2
Research and discover new mathematical ideas
+Set aside four focused hours to explore the conjecture about spectral gaps, draft a rigorous outline of…
Research and discover new mathematical ideas
+Set aside four focused hours to explore the conjecture about spectral gaps, draft a rigorous outline of potential approaches, run symbolic experiments on key lemmas, and save a short note with conjectures and counterexample ideas for discussion with colleagues.
The tools that do the workBashESCOO*NETWikipedia
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Design mathematical models to interpret data
+Build a parsimonious model linking the survey covariates to response variance, derive the likelihood and…
Design mathematical models to interpret data
+Build a parsimonious model linking the survey covariates to response variance, derive the likelihood and diagnostics, fit parameters to the dataset, then produce residual plots and a one‑page summary recommending which predictors to retain.
The tools that do the workIBM SPSS Statisticsjob descriptionsWikipedia
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The daily work16
Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
+Write a clear 1,500–2,000 word report of my recent results on random matrix limits, include theorem…
Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
+Write a clear 1,500–2,000 word report of my recent results on random matrix limits, include theorem statements, sketch proofs, related work citations, and a two-paragraph lay summary for the departmental newsletter by next Tuesday.
The tools that do the workLinuxO*NET
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Assemble sets of assumptions, and explore the consequences of each set.
+List five distinct assumption sets for the continuum percolation model, for each derive the primary…
Assemble sets of assumptions, and explore the consequences of each set.
+List five distinct assumption sets for the continuum percolation model, for each derive the primary consequences, note which lemmas fail, and produce a short advice paragraph on which set to use for a conference submission tomorrow.
The tools that do the workC++O*NET
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Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
+Prepare a polished draft that formalises the relationships between curvature, spectral gap, and growth rate…
Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
+Prepare a polished draft that formalises the relationships between curvature, spectral gap, and growth rate using precise definitions, worked symbolic derivations, and three illustrative examples aimed at the analysis seminar next week.
The tools that do the workC#O*NET
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Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
+Develop a technical note outlining a new encryption scheme: define the algorithm, prove basic security…
Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
+Develop a technical note outlining a new encryption scheme: define the algorithm, prove basic security properties under clear hardness assumptions, and produce test vectors and a short implementation guide for the applied cryptography group meeting in two weeks.
The tools that do the workC++O*NET
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Compile charts and graphs for data presentation
+Create a set of publication-quality charts showing eigenvalue distributions, convergence rates, and parameter…
Compile charts and graphs for data presentation
+Create a set of publication-quality charts showing eigenvalue distributions, convergence rates, and parameter sensitivity with captions and data sources, export as print-ready images for the conference poster due Friday.
The tools that do the workIBM SPSS Statisticsjob descriptions
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Identify problems through discussion with colleagues or clients
+Summarise the problem points from yesterday's group meeting with Anna, Miguel, and Priya: list the three open…
Identify problems through discussion with colleagues or clients
+Summarise the problem points from yesterday's group meeting with Anna, Miguel, and Priya: list the three open questions they raised, the proposed solutions, who owns each action, and deadlines for follow-up by next Monday.
The tools that do the workLinuxjob descriptions
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Collect data from statistical or experimental sources
+Gather the experimental and observational datasets from the university lab logs, the public repository at…
Collect data from statistical or experimental sources
+Gather the experimental and observational datasets from the university lab logs, the public repository at Stanford, and my colleague Nadia’s CSV exports, check variable definitions and missing-data rates, then combine into one cleaned analysis table for model fitting by Friday.
The tools that do the workLinuxjob descriptions
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Design experiments and research projects
+Draft the research plan for the summer project: state the hypothesis on random matrix spectra, list three…
Design experiments and research projects
+Draft the research plan for the summer project: state the hypothesis on random matrix spectra, list three experimental setups with sample sizes and sampling protocols, predefine primary and secondary outcomes, and a two-month timeline to present to the grant committee.
The tools that do the workIBM SPSS Statisticsjob descriptions
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Analyze results to provide insights in various fields
+Take the cleaned analysis table, run the planned statistical tests and regression diagnostics, summarise…
Analyze results to provide insights in various fields
+Take the cleaned analysis table, run the planned statistical tests and regression diagnostics, summarise significant effects with confidence intervals and assumptions checks, then write a two-page insight memo linking results to cryptography and fluid dynamics problems.
The tools that do the workIBM SPSS StatisticsLinuxjob descriptions
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Derive corollaries from theorems
+From the main paper’s theorem on spectral gaps, derive and write three corollaries with proofs, state…
Derive corollaries from theorems
+From the main paper’s theorem on spectral gaps, derive and write three corollaries with proofs, state required assumptions clearly, and note any counterexamples or boundary cases to discuss at Monday’s seminar.
The tools that do the workLinuxWikipedia
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Calculate areas, volumes, and surface areas of shapes
+Compute exact formulas and numeric examples for areas, volumes and surface areas of the three curved solids…
Calculate areas, volumes, and surface areas of shapes
+Compute exact formulas and numeric examples for areas, volumes and surface areas of the three curved solids in section two, include derivations, produce high-precision numerical checks for each shape, and assemble the results for the methods appendix.
The tools that do the workC++Wikipedia
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Approximate mathematical constants such as π
+Implement and test three algorithms to approximate pi to 12 decimal places, compare convergence rates and…
Approximate mathematical constants such as π
+Implement and test three algorithms to approximate pi to 12 decimal places, compare convergence rates and runtime, document the code and results, and attach the fastest implementation to the supplementary materials.
The tools that do the workC++Wikipedia
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Develop methods like exhaustion for calculations
+Create a rigorous method of exhaustion for my new family of integrals: state assumptions, construct nested…
Develop methods like exhaustion for calculations
+Create a rigorous method of exhaustion for my new family of integrals: state assumptions, construct nested approximating sequences, prove convergence bounds to within 10^-6 on the unit interval, and produce worked examples for the paper due next Tuesday.
The tools that do the workC++Wikipedia
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Apply knowledge to engineering and scientific challenges
+Translate the abstract operator identities into engineering-ready formulas: derive closed-form…
Apply knowledge to engineering and scientific challenges
+Translate the abstract operator identities into engineering-ready formulas: derive closed-form approximations, quantify error terms for 95% confidence in structural load estimates, and prepare three example applications for the grant review on Friday.
The tools that do the workC++ESCO
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Conduct quantitative research
+Run a quantitative study of the proposed stochastic model: simulate 10,000 realizations, compute sample…
Conduct quantitative research
+Run a quantitative study of the proposed stochastic model: simulate 10,000 realizations, compute sample moments and asymptotic variances, perform hypothesis tests at 5% and export the summary tables for the methods section by Wednesday.
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Think analytically
+Analyze this set of propositions for structural weaknesses: produce step-by-step logical reductions, identify…
Think analytically
+Analyze this set of propositions for structural weaknesses: produce step-by-step logical reductions, identify hidden assumptions, and rank three alternative lemmas by ease of proof and impact on the main theorem before our group meeting Thursday.
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Says who?
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Activities this job lives in
The human activities behind the tasks — each with its honest AI ceiling.
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Shared with other careers — the same record means something different in each.
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Same family of work — each with its own tasks and prompts.
The LLOS Work Atlas is the world's largest evidenced task library — a map of human work, with a ready prompt behind every task. 1,774 careers · every task named by the sources that witnessed it — O*NET, ESCO, real job descriptions, Wikipedia — and the deepest tasks by several at once. And it is honest about limits: where AI cannot help, the map says so.
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Built on public evidence: O*NET®, ESCO, Wikipedia, U.S. Bureau of Labor Statistics, ILOSTAT. All sources & licenses
Built on public evidence: O*NET®, ESCO, Wikipedia, U.S. Bureau of Labor Statistics, ILOSTAT. All sources & licenses