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.
Analysing3
Perform actuarial computations
+Run the full set of life‑table and loss‑development calculations on the portfolio claims file, produce a…
Perform actuarial computations
+Run the full set of life‑table and loss‑development calculations on the portfolio claims file, produce a one‑page summary of reserves by line with sensitivity to discount rate ±1%, and export the numeric tables for audit.
The tools that do the workC++job descriptionsO*NETWikipedia
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Research and discover new mathematical ideas
+Scan recent literature and run exploratory computations to test whether a proposed operator on Sobolev spaces…
Research and discover new mathematical ideas
+Scan recent literature and run exploratory computations to test whether a proposed operator on Sobolev spaces yields a new compactness criterion; draft a 1,000‑word research note with conjectures, counterexamples tried, and next experiments for the group meeting.
The tools that do the workC++ESCOO*NETWikipedia
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Design mathematical models to interpret data
+Build a stochastic model that links sensor time series to incident risk, fit it to the last three years of…
Design mathematical models to interpret data
+Build a stochastic model that links sensor time series to incident risk, fit it to the last three years of cleaned data, produce parameter estimates with confidence intervals, and deliver a two‑page interpretation for the product team.
The tools that do the workIBM SPSS Statisticsjob descriptionsWikipedia
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Learning1
Mentor others on mathematical techniques
+Prepare three mentoring problems: one on measure‑theoretic probability, one on PDE methods for option…
Mentor others on mathematical techniques
+Prepare three mentoring problems: one on measure‑theoretic probability, one on PDE methods for option pricing, and one on statistical inference for censored data; include model solutions, suggested readings, and a 60‑minute workshop plan for Sarah and Mateo.
The tools that do the workLinuxjob descriptionsO*NETWikipedia
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The daily work16
Develop methods like exhaustion for calculations
+Derive and write up a sequence of exhaustion-style approximation methods to estimate the integral and…
Develop methods like exhaustion for calculations
+Derive and write up a sequence of exhaustion-style approximation methods to estimate the integral and eigenvalue bounds for the new plate vibration model, include assumptions, error bounds, and one worked numeric example for review by Dr. Patel on Friday.
The tools that do the workC++Wikipedia
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Apply knowledge to engineering and scientific challenges
+Translate the beam buckling case into solvable model equations, produce closed-form approximations where…
Apply knowledge to engineering and scientific challenges
+Translate the beam buckling case into solvable model equations, produce closed-form approximations where possible and a calibrated numerical solver for the prototype, then deliver a short note with predicted safety margins to the engineering lead by Wednesday.
The tools that do the workC++ESCO
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Conduct quantitative research
+Design and run the quantitative study to estimate parameter distributions for the thermal diffusion project,…
Conduct quantitative research
+Design and run the quantitative study to estimate parameter distributions for the thermal diffusion project, prepare cleaned datasets, monte carlo uncertainty analysis, and a methods appendix so the PI can include results in the grant update next Tuesday.
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Think analytically
+Work through the anomalous residuals from last month's model, produce three competing analytical explanations…
Think analytically
+Work through the anomalous residuals from last month's model, produce three competing analytical explanations with supporting simplified calculations, and flag which follow-up experiments would discriminate between them before Friday's group meeting.
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Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
+Write and circulate a three-page research brief on our latest modelling of epidemic spread, prepare a short…
Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
+Write and circulate a three-page research brief on our latest modelling of epidemic spread, prepare a short manuscript suitable for a journal, and draft a 12-minute conference talk with slides for the SIAM meeting next month.
The tools that do the workLinuxO*NET
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Assemble sets of assumptions, and explore the consequences of each set.
+List three coherent assumption sets for the fluid dynamics model, run sensitivity runs for each set over the…
Assemble sets of assumptions, and explore the consequences of each set.
+List three coherent assumption sets for the fluid dynamics model, run sensitivity runs for each set over the next 48 hours, and summarise how equilibrium solutions shift in a one-page memo for the modelling team.
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.
+Derive the governing equations relating the measured variables, simplify using nondimensionalisation, and…
Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
+Derive the governing equations relating the measured variables, simplify using nondimensionalisation, and produce worked examples showing how scaling alters expected solutions for the methods appendix.
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.
+Design a new cipher framework for secure telemetry, analyse its resistance to known plaintext and chosen…
Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
+Design a new cipher framework for secure telemetry, analyse its resistance to known plaintext and chosen ciphertext attacks, and produce a technical note with proofs and complexity estimates for the security review board.
The tools that do the workC++O*NET
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Compile charts and graphs for data presentation
+Compile clear charts showing model output versus observations, label axes and uncertainty bands, and produce…
Compile charts and graphs for data presentation
+Compile clear charts showing model output versus observations, label axes and uncertainty bands, and produce a single-page figure pack for the stakeholder briefing on Friday morning.
The tools that do the workIBM SPSS Statisticsjob descriptions
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Identify problems through discussion with colleagues or clients
+Meet with Dr. Lane and the policy analyst at 10 a.m., list the three priority problems they describe, map…
Identify problems through discussion with colleagues or clients
+Meet with Dr. Lane and the policy analyst at 10 a.m., list the three priority problems they describe, map them to modelling tasks and risks, and send a one-page action plan by 4 p.m.
The tools that do the workApple macOSjob descriptions
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Collect data from statistical or experimental sources
+Gather temperature, pressure and sensor-readings from the last two field trials and the central lab dataset,…
Collect data from statistical or experimental sources
+Gather temperature, pressure and sensor-readings from the last two field trials and the central lab dataset, merge into one cleaned CSV with timestamps aligned and missing values flagged, then summarise quality issues and data provenance.
The tools that do the workLinuxjob descriptions
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Design experiments and research projects
+Draft the experimental plan to test diffusion rates: state hypotheses, list controllable variables, required…
Design experiments and research projects
+Draft the experimental plan to test diffusion rates: state hypotheses, list controllable variables, required sample sizes with power calculations, measurement procedures, and a two-week schedule for the pilot run.
The tools that do the workIBM SPSS Statisticsjob descriptions
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Analyze results to provide insights in various fields
+Run the statistical analysis on the completed trial: compute effect sizes, confidence intervals and model…
Analyze results to provide insights in various fields
+Run the statistical analysis on the completed trial: compute effect sizes, confidence intervals and model residuals, test assumptions, produce a one-page interpretation linking results to engineering tolerances and next recommended actions.
The tools that do the workIBM SPSS Statisticsjob descriptions
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Derive corollaries from theorems
+From the proved theorem on convergence rates, derive and write three practical corollaries showing bounds…
Derive corollaries from theorems
+From the proved theorem on convergence rates, derive and write three practical corollaries showing bounds under weaker smoothness, include constructive proofs and notes on where constants tighten for applied models.
The tools that do the workC++Wikipedia
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Calculate areas, volumes, and surface areas of shapes
+Compute exact areas, volumes and surface areas for the listed composite shapes, show the integration steps,…
Calculate areas, volumes, and surface areas of shapes
+Compute exact areas, volumes and surface areas for the listed composite shapes, show the integration steps, numeric answers to three significant figures, and package the worked solutions in one PDF for the design team.
The tools that do the workC++Wikipedia
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Approximate mathematical constants such as π
+Implement and run three algorithms to approximate pi to twelve decimal places, report convergence rates and…
Approximate mathematical constants such as π
+Implement and run three algorithms to approximate pi to twelve decimal places, report convergence rates and runtime on the desktop, and attach the source and short notes on numerical stability.
The tools that do the workC++Wikipedia
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Activities this job lives in
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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