Mathematicians
15-2021.00Median wage $126,710/yr2,030 employed (US)Rank #187 of 923 scored · top 20% by substitution
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.
Sub-scores
0–100 · band = confidence interval from rater disagreement
Substitution39
Exposure32
Augmentation75
Substitution — the headline: capability discounted by cost, barriers and adoption.
Exposure — technical capability alone, regardless of whether anyone deploys it.
Augmentation — how much AI assists without replacing. High here + moderate substitution = a changing job, not a disappearing one.
Tasks on the substitution scale
12 rated tasks, binned by substitution score.
Position among all scored occupations
Distribution of 923 occupation scores; the marker is this occupation.
Tasks with substitution ≥ 70
8%
Run 1.0.0-draft.1 · computed 2026-08-05 · rater panel: claude-sonnet-5, claude-haiku-4-5-20251001 · intervals span rater disagreement.
Why this score
The five weighted dimensions of the composite, averaged across this occupation's tasks (importance-weighted, panel mean). Exact weights and formulas: /api/v1/methodology.
Task automatabilityw 35%33
panel mean rating 2.3/5 → substitution pressure 33/100
Technical feasibility todayw 20%32
panel mean rating 2.3/5 → substitution pressure 32/100
Cost vs. human wagew 15%40
panel mean rating 2.6/5 → substitution pressure 40/100
Adoption barriersw 20%inverted — strong barriers lower the score56
panel mean rating 2.7/5 (barrier strength) → substitution pressure 56/100
Sector adoption velocityw 10%42
panel mean rating 2.7/5 → substitution pressure 42/100
Task breakdown (12 tasks)
Substitution pressure per task, weighted by O*NET importance in the composite. Expand a task for the full rater audit trail — every rating, every model, every rationale.
Perform computations and apply methods of numerical analysis to data.
85CI 79–91 · exposure 80 · augmentation 100 · importance 3.9/5 · click for rater detail
Perform computations and apply methods of numerical analysis to data.
85| Dimension | Model | Rating | Rationale |
|---|---|---|---|
| Sector adoption velocity | claude-haiku-4-5-20251001 | 5/5 | Adoption is near-universal and decades-mature in tech, finance, engineering, and research sectors. Nearly all mathematicians and scientists now rely on automated numerical tools as a core part of their workflow, not new pilots. |
| Sector adoption velocity | claude-sonnet-5 | 4/5 | Scientific computing, finance, and engineering sectors have deeply integrated automated numerical tools and increasingly AI-assisted coding for decades, representing fast, mature adoption. |
| Augmentation potential | claude-haiku-4-5-20251001 | 5/5 | AI-powered numerical tools fundamentally augment mathematician productivity by handling routine computation, freeing cognitive effort for problem formulation, method selection, and interpretation. This is the dominant mode of work in modern applied mathematics. |
| Augmentation potential | claude-sonnet-5 | 5/5 | AI coding assistants and computational tools substantially speed up setting up, debugging, and executing numerical analysis, letting mathematicians focus on method selection and interpretation. |
| Task automatability | claude-haiku-4-5-20251001 | 4/5 | Current AI and symbolic computation tools (Wolfram Alpha, SymPy, automated theorem provers) can execute most standard numerical analysis methods—integration, differentiation, linear algebra, FFT—with high speed and accuracy. However, applying the *right* method to novel problem classes and interpreting results for non-routine scenarios still requires human mathematical judgment, preventing a full 5 rating. |
| Task automatability | claude-sonnet-5 | 4/5 | Numerical computation and standard numerical analysis methods (root-finding, interpolation, optimization, linear algebra) are highly amenable to automation via existing software libraries and AI tools that can write/execute code, meeting the 50% time-saving bar for most routine cases. |
| Adoption barriers | claude-haiku-4-5-20251001 | 2/5 | Few legal or regulatory barriers exist to automating pure numerical computation; organizations can and do substitute software freely. Minor friction remains in verification/validation and trust in results for mission-critical applications, but nothing prevents the substitution. |
| Adoption barriers | claude-sonnet-5 | 1/5 | No licensing, liability, or regulatory requirement mandates a human perform numerical computations; software has long been the default tool. |
| Cost vs. human wage | claude-haiku-4-5-20251001 | 5/5 | Cloud-based or open-source numerical computation is orders of magnitude cheaper per computation than paying a mathematician's loaded hourly rate ($80–150+/hr). Even licensed software is cheap per operation once amortized. |
| Cost vs. human wage | claude-sonnet-5 | 5/5 | Computational execution is extremely cheap relative to a mathematician's time once the method is specified, often orders of magnitude cheaper for the raw computation step. |
| Technical feasibility today | claude-haiku-4-5-20251001 | 5/5 | Mature, production-grade systems (Mathematica, MATLAB, Python scientific stack with numpy/scipy, cloud compute services) reliably perform numerical computations at scale. These are deployed across academia, industry, and research institutions and have been for decades. |
| Technical feasibility today | claude-sonnet-5 | 4/5 | Mature tools (MATLAB, NumPy/SciPy, Wolfram Alpha) plus AI coding assistants and code-execution agents reliably perform numerical computations in production today, though complex or novel numerical methods still require expert oversight. |
Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
64CI 61–66 · exposure 50 · augmentation 100 · importance 3.9/5 · click for rater detail
Address the relationships of quantities, magnitudes, and forms through the use of numbers and symbols.
64| Dimension | Model | Rating | Rationale |
|---|---|---|---|
| Sector adoption velocity | claude-haiku-4-5-20251001 | 4/5 | AI-assisted mathematics tools are rapidly adopted in academic and industry research (finance, engineering, science), with widespread use of CAS, proof assistants, and LLM copilots for exploratory work and code generation. Adoption is deepening in information-intensive sectors. |
| Sector adoption velocity | claude-sonnet-5 | 4/5 | Mathematical and scientific research fields have rapidly adopted computational and AI-assisted tools for symbolic and numerical work, following broader trends in professional/technical services. |
| Augmentation potential | claude-haiku-4-5-20251001 | 5/5 | AI systems substantially augment mathematician productivity by handling symbolic manipulation, generating candidate proofs, testing conjectures, and suggesting reformulations—all while keeping the human mathematician in the loop for validation and creative direction. This is one of the clearest cases of high augmentation. |
| Augmentation potential | claude-sonnet-5 | 5/5 | AI dramatically augments mathematicians by handling symbolic computation, checking proofs, and exploring conjectures, letting humans focus on higher-level insight and interpretation. |
| Task automatability | claude-haiku-4-5-20251001 | 3/5 | Current AI systems (particularly LLMs and symbolic math engines) can handle routine algebraic manipulation, equation solving, and some symbolic reasoning, but struggle with novel proof discovery and deep mathematical insight requiring human creativity. Roughly half of routine mathematical work—computation, verification, pattern application—can be automated with significant setup and oversight. |
| Task automatability | claude-sonnet-5 | 3/5 | AI systems (e.g., theorem provers, computer algebra systems, LLMs) can manipulate symbols and solve many quantitative relationship problems, but genuine novel mathematical research and deep proof insight still require human judgment. |
| Adoption barriers | claude-haiku-4-5-20251001 | 2/5 | Few regulatory or licensing barriers exist for automating mathematical computation itself; organizations can freely deploy symbolic solvers. The main barrier is organizational inertia and the requirement for human mathematicians to validate novel results, not legal prohibition. |
| Adoption barriers | claude-sonnet-5 | 1/5 | No licensing or regulatory requirement mandates human performance of mathematical symbol manipulation; usage of computational tools is already standard and unrestricted. |
| Cost vs. human wage | claude-haiku-4-5-20251001 | 4/5 | AI inference for symbolic math is very cheap per computation compared to paying a mathematician's fully-loaded salary for routine calculations and verifications. However, the cost advantage diminishes for creative research and proof validation where human oversight and deep expertise remain essential. |
| Cost vs. human wage | claude-sonnet-5 | 4/5 | For routine symbolic/numeric manipulation, AI tools are vastly cheaper than a mathematician's time, though complex novel work still needs costly human oversight. |
| Technical feasibility today | claude-haiku-4-5-20251001 | 3/5 | Deployed products like Wolfram Alpha, ChatGPT, and specialized CAS tools reliably perform computational and routine symbolic tasks, but error rates rise sharply on non-standard problems and novel mathematical reasoning. These products work well within narrow, well-defined domains but lack the generality for comprehensive mathematical research. |
| Technical feasibility today | claude-sonnet-5 | 3/5 | Deployed tools like Wolfram Alpha, Mathematica, and LLM-based math assistants reliably handle routine symbolic manipulation and standard problems, but struggle with cutting-edge, open-ended mathematical research. |
Assemble sets of assumptions, and explore the consequences of each set.
58CI 35–81 · exposure 58 · augmentation 88 · importance 4.0/5 · click for rater detail
Assemble sets of assumptions, and explore the consequences of each set.
58| Dimension | Model | Rating | Rationale |
|---|---|---|---|
| Sector adoption velocity | claude-haiku-4-5-20251001 | 3/5 | Academic mathematics and research institutions are adopting AI-assisted proof and symbolic exploration tools at a moderate pace, with many pilots and growing use in graduate education, but full production replacement remains limited. Adoption is faster in applied fields (engineering, finance modeling) than pure research mathematics. |
| Sector adoption velocity | claude-sonnet-5 | 2/5 | Mathematics research is a small, specialized field with slow, uneven AI tool adoption compared to industries like finance or software engineering. |
| Augmentation potential | claude-haiku-4-5-20251001 | 5/5 | AI systems substantially augment mathematicians by rapidly generating candidate assumptions, exploring multiple solution branches in parallel, and highlighting logical consequences that might otherwise be missed. This keeps the human researcher in the loop while multiplying their productive output. |
| Augmentation potential | claude-sonnet-5 | 4/5 | AI (symbolic computation, theorem provers, LLMs) substantially helps mathematicians test consequences of assumptions, generate conjectures, and check special cases, meaningfully boosting productivity while the mathematician retains control. |
| Task automatability | claude-haiku-4-5-20251001 | 5/5 | Current AI systems can readily generate plausible sets of mathematical assumptions and derive their logical consequences through symbolic computation, proof search, and automated reasoning. Large language models combined with computer algebra systems can perform this end-to-end workflow with significant time savings over manual derivation. |
| Task automatability | claude-sonnet-5 | 2/5 | This is a creative research task requiring judgment about which assumptions are mathematically interesting or fruitful; AI can help explore consequences symbolically but cannot autonomously originate and select meaningful assumption sets end-to-end at expert quality.the human still drives the exploration. |
| Adoption barriers | claude-haiku-4-5-20251001 | 2/5 | Few legal or regulatory barriers prevent AI-assisted or automated assumption exploration in pure mathematics. Academic and institutional inertia may slow adoption, but no licensing requirement mandates human mathematicians for this specific task. |
| Adoption barriers | claude-sonnet-5 | 2/5 | No licensing requirement, but institutional/peer-review norms and the need for rigorous proof verification create some friction against trusting AI-generated exploratory conclusions. |
| Cost vs. human wage | claude-haiku-4-5-20251001 | 4/5 | AI inference cost for assumption exploration and consequence derivation is substantially cheaper than paying a mathematician's loaded wage, especially when amortized across multiple exploration runs. Cloud-based theorem provers and LLMs cost pennies per task versus hundreds per hour for human labor. |
| Cost vs. human wage | claude-sonnet-5 | 2/5 | AI tools are cheap per query but require substantial expert oversight and verification for correctness in research mathematics, so all-in cost savings versus a trained mathematician are modest. |
| Technical feasibility today | claude-haiku-4-5-20251001 | 4/5 | Deployed systems like theorem provers (Coq, Lean with AI assistance), symbolic math engines (Mathematica, SymPy), and LLMs with code execution can reliably assemble assumptions and explore consequences for well-defined mathematical domains. However, reliability degrades for novel or highly abstract problem domains requiring creative insight. |
| Technical feasibility today | claude-sonnet-5 | 2/5 | Computer algebra systems and LLMs can perform symbolic manipulation and check some logical consequences, but no deployed product reliably performs open-ended assumption exploration for novel mathematical research at production quality. |
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
50CI 32–67 · exposure 45 · augmentation 88 · importance 3.7/5 · click for rater detail
Apply mathematical theories and techniques to the solution of practical problems in business, engineering, the sciences, or other fields.
50| Dimension | Model | Rating | Rationale |
|---|---|---|---|
| Sector adoption velocity | claude-haiku-4-5-20251001 | 3/5 | Adoption is uneven: finance and tech sectors actively deploy AI-assisted math and proof-checking tools, but many academic and traditional engineering environments remain conservative and skeptical of full automation. Pilots are common, but deep production displacement of mathematical work is not yet universal. |
| Sector adoption velocity | claude-sonnet-5 | 3/5 | Adoption of AI-assisted computation and modeling tools is growing steadily in engineering, finance, and scientific fields, though full task automation remains rare and pilot-stage. |
| Augmentation potential | claude-haiku-4-5-20251001 | 5/5 | AI systems (symbolic engines, numerical solvers, proof assistants, visualization tools) substantially amplify mathematician productivity by handling tedious algebra, computation, and exploration, while humans retain control over problem selection, strategy, and validation. This is one of the clearest examples of human-AI augmentation in professional work. |
| Augmentation potential | claude-sonnet-5 | 4/5 | AI significantly accelerates literature review, symbolic manipulation, code generation, and exploratory computation, meaningfully boosting mathematician productivity while the human retains problem framing and validation. |
| Task automatability | claude-haiku-4-5-20251001 | 4/5 | Current AI systems can handle significant portions of mathematical problem formulation, symbolic computation, numerical analysis, and verification. However, the 'practical problem' framing often requires domain judgment and context-setting that remains difficult for AI; end-to-end automation of the full solution pipeline from real-world problem to validated implementation still falls short of reliable 50% time savings for complex novel problems. |
| Task automatability | claude-sonnet-5 | 2/5 | AI can assist with formal derivations, symbolic computation, and coding for well-posed subproblems, but framing novel practical problems mathematically and validating the approach requires human judgment not yet reliably automatable end-to-end.' |
| Adoption barriers | claude-haiku-4-5-20251001 | 3/5 | Some organizational friction exists: mathematicians often must validate and interpret AI results, and liability concerns mean human sign-off is common in safety-critical domains (aerospace, finance). However, no strict licensing requirement forces a human to perform the math itself, so barriers are moderate rather than hard. |
| Adoption barriers | claude-sonnet-5 | 2/5 | No licensing requirement gates this work, but organizations still rely on credentialed expertise and human validation for high-stakes technical modeling, creating moderate professional friction. |
| Cost vs. human wage | claude-haiku-4-5-20251001 | 4/5 | Computational inference is extremely cheap relative to mathematician labor (often $100+ per hour loaded cost), and symbolic/numerical computation can be parallelized. Integration and oversight overhead exist but are modest for well-structured problems, making AI 5–20× cheaper per solved problem in many engineering and science contexts. |
| Cost vs. human wage | claude-sonnet-5 | 2/5 | For narrow computational subtasks AI is cheap, but the overall task still requires substantial expert oversight and iteration, keeping all-in cost comparable to or only modestly below human cost. |
| Technical feasibility today | claude-haiku-4-5-20251001 | 3/5 | Mature products (Wolfram Language, SymPy, computational platforms) perform well-defined mathematical tasks reliably in production, but they require careful problem setup and verification. For open-ended problem solving in unfamiliar domains, AI-based systems still have material error rates and narrow scope relative to expert mathematicians. |
| Technical feasibility today | claude-sonnet-5 | 2/5 | Tools like Wolfram Alpha, code interpreters, and LLM math assistants handle bounded computations but no deployed product reliably formulates and solves open-ended applied mathematical problems in production. |
Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
34CI 30–38 · exposure 25 · augmentation 75 · importance 3.7/5 · click for rater detail
Develop mathematical or statistical models of phenomena to be used for analysis or for computational simulation.
34| Dimension | Model | Rating | Rationale |
|---|---|---|---|
| Sector adoption velocity | claude-haiku-4-5-20251001 | 2/5 | While tech and quantitative finance firms are experimenting with AI-assisted model development, widespread production adoption remains limited. Most academic and research institutions are in pilot phases rather than systematic deployment. |
| Sector adoption velocity | claude-sonnet-5 | 3/5 | Quantitative fields (finance, data science, academia) show fast adoption of AI coding/analysis assistants, though full model-development workflows remain human-led with AI as a pilot-stage aid. |
| Augmentation potential | claude-haiku-4-5-20251001 | 4/5 | AI systems demonstrably assist mathematicians and statisticians through code generation, symbolic manipulation, literature synthesis, and rapid prototyping of candidate models, significantly accelerating the exploration phase while humans retain control over conceptual direction and validation. |
| Augmentation potential | claude-sonnet-5 | 4/5 | AI substantially accelerates literature review, code generation, symbolic manipulation, and exploratory analysis, meaningfully boosting mathematician productivity while humans retain core modeling judgment. |
| Task automatability | claude-haiku-4-5-20251001 | 2/5 | While AI can assist in generating mathematical formulations and fitting statistical models, developing novel models of complex phenomena typically requires deep domain expertise, creative hypothesis formation, and iterative refinement based on domain knowledge that current systems struggle with end-to-end. AI tools can automate parts (e.g., parameter estimation, code generation) but the core modeling architecture and validation remain primarily human-driven. |
| Task automatability | claude-sonnet-5 | 2/5 | AI can assist with formulating and coding models but developing novel mathematical/statistical models for complex phenomena requires deep domain judgment, creativity, and validation that current AI cannot reliably perform end-to-end. |
| Adoption barriers | claude-haiku-4-5-20251001 | 3/5 | Publishing and validation norms require human authorship and accountability for model correctness; organizational structures typically assign ownership to human researchers. However, these are soft rather than hard legal/licensing barriers, allowing gradual AI integration. |
| Adoption barriers | claude-sonnet-5 | 2/5 | No licensing requirement blocks AI use, though organizations still require expert sign-off on model validity for high-stakes analysis, creating moderate but not hard barriers. |
| Cost vs. human wage | claude-haiku-4-5-20251001 | 2/5 | Current AI infrastructure costs (compute, integration, validation oversight) are still comparable to or exceed the cost of a mathematician's time for model development work, especially given the need for human review and refinement of AI-generated models. |
| Cost vs. human wage | claude-sonnet-5 | 2/5 | AI can cheaply generate boilerplate code or suggest standard model forms, but the expert time needed to validate, adapt, and ensure correctness for novel applications keeps overall costs comparable to or only modestly below human-only work. |
| Technical feasibility today | claude-haiku-4-5-20251001 | 2/5 | Products exist for narrow model-fitting tasks (AutoML platforms, symbolic regression tools) but no deployed system reliably develops novel mathematical or statistical models of new phenomena from scratch with minimal human guidance. Existing tools require extensive human direction and validation. |
| Technical feasibility today | claude-sonnet-5 | 2/5 | Deployed tools (Copilot, ChatGPT, Wolfram Alpha) help draft equations or code for known model classes, but no production system reliably develops original models for novel phenomena without heavy expert oversight. |
Mentor others on mathematical techniques.
33CI 30–36 · exposure 25 · augmentation 75 · importance 4.3/5 · click for rater detail
Mentor others on mathematical techniques.
33| Dimension | Model | Rating | Rationale |
|---|---|---|---|
| Sector adoption velocity | claude-haiku-4-5-20251001 | 2/5 | Educational institutions and research labs are slow to adopt AI as a replacement for human mentorship, viewing it as a supplementary tool rather than a substitute. Adoption remains experimental and piecemeal rather than systematic. |
| Sector adoption velocity | claude-sonnet-5 | 3/5 | Academic and research math environments are moderately adopting AI as a study/explanation aid, but formal mentoring relationships remain largely human-driven with slow structural change. |
| Augmentation potential | claude-haiku-4-5-20251001 | 4/5 | AI can meaningfully augment human mentors by generating worked examples, providing instant reference materials, and drafting explanations that mentors can then personalize and refine. This leaves the mentor in control while raising their productivity in content preparation and explanation delivery. |
| Augmentation potential | claude-sonnet-5 | 4/5 | AI can significantly help mentors by generating examples, explaining alternative approaches, and checking mentees' work, boosting productivity while the human retains the mentoring role. |
| Task automatability | claude-haiku-4-5-20251001 | 2/5 | Mentoring involves personalized feedback, assessing understanding gaps, and adapting explanations—nuanced tasks that require human judgment and emotional intelligence. Current AI can generate explanations of techniques but cannot reliably assess a mentee's conceptual gaps or provide the sustained, adaptive guidance that characterizes effective mentoring. |
| Task automatability | claude-sonnet-5 | 2/5 | Mentoring involves personalized guidance, relationship-building, and adaptive judgment about a mentee's development that current AI cannot replicate end-to-end, though AI can explain techniques on demand.6 |
| Adoption barriers | claude-haiku-4-5-20251001 | 3/5 | Academic and professional settings often prefer human mentorship for career guidance and relationship-building, creating organizational friction. However, there are no strict licensing or legal barriers preventing AI-assisted mentoring, only preference and cultural norms. |
| Adoption barriers | claude-sonnet-5 | 3/5 | No licensing requirement bars AI from explaining math, but institutional norms, trust, and career-development expectations create real friction against full substitution of human mentors. |
| Cost vs. human wage | claude-haiku-4-5-20251001 | 2/5 | AI tutoring systems have marginal inference costs but require significant content curation and oversight. A senior mathematician's mentoring labor remains expensive, but the quality and personalization gap means AI is not yet cost-competitive for equivalent mentoring value. |
| Cost vs. human wage | claude-sonnet-5 | 3/5 | AI tools are cheap per query, but true mentoring requires ongoing human time and judgment, so the effective cost comparison for full mentoring is roughly comparable rather than dramatically cheaper. |
| Technical feasibility today | claude-haiku-4-5-20251001 | 2/5 | Chatbots can explain mathematical concepts and tutoring products exist, but they lack the ability to build relationships, detect subtle misunderstandings, or adjust pedagogical strategy based on a mentee's progress over time. No deployed product reliably replaces a human mentor in this role. |
| Technical feasibility today | claude-sonnet-5 | 2/5 | Chatbots and tutoring tools can explain mathematical concepts, but no deployed product substitutes for the sustained, relational mentoring role among professional mathematicians. |
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
32CI 28–38 · exposure 25 · augmentation 75 · importance 3.2/5 · click for rater detail
Develop computational methods for solving problems that occur in areas of science and engineering or that come from applications in business or industry.
32| Dimension | Model | Rating | Rationale |
|---|---|---|---|
| Sector adoption velocity | claude-haiku-4-5-20251001 | 3/5 | Research organizations use AI-assisted coding tools in computational method development pipelines, but wholesale replacement of the method-development process itself remains rare. Adoption is mixed: tech-forward labs experiment with AI assistance, while traditional mathematics and engineering departments adopt more conservatively. |
| Sector adoption velocity | claude-sonnet-5 | 3/5 | Applied math, engineering, and quantitative business sectors are adopting AI tools for computation and modeling assistance at a moderate pace, with pilots more common than full production reliance for method development. |
| Augmentation potential | claude-haiku-4-5-20251001 | 4/5 | AI significantly augments mathematician productivity through code generation, algorithm prototyping, debugging, and literature/data search, while the human retains full responsibility for problem conception and method validation. This represents a mature augmentation pattern in applied mathematics and computational science. |
| Augmentation potential | claude-sonnet-5 | 4/5 | AI substantially aids literature review, code generation, symbolic manipulation, and testing of candidate approaches, meaningfully speeding up the exploratory phase of method development while mathematicians retain core judgment. |
| Task automatability | claude-haiku-4-5-20251001 | 2/5 | Developing novel computational methods requires creative problem formulation, research intuition, and deep domain understanding that current AI cannot replicate end-to-end. While AI can assist with code generation and algorithm implementation, the core task of conceiving new mathematical approaches and validating them scientifically remains beyond current AI capabilities without substantial human direction. |
| Task automatability | claude-sonnet-5 | 2/5 | AI can assist in drafting algorithms, code, or exploring known methods, but developing genuinely novel computational methods for complex applied problems requires deep domain judgment, creativity, and validation that current AI cannot reliably perform end-to-end. |
| Adoption barriers | claude-haiku-4-5-20251001 | 4/5 | Strong barriers exist: novel computational methods require peer review, publication, and often regulatory or contractual validation before deployment, especially in regulated industries (finance, healthcare, aerospace). The human mathematician must typically be credited and accountable for the method's correctness and applicability, creating legal and professional gatekeeping. |
| Adoption barriers | claude-sonnet-5 | 2/5 | No formal licensing barrier exists, but organizational trust, need for rigorous proof/validation, and reliance on domain expertise create moderate friction against full automation. |
| Cost vs. human wage | claude-haiku-4-5-20251001 | 2/5 | AI tools for code generation and prototyping reduce some overhead but cannot replace the mathematician's labor for the core intellectual work of method development. The cost of AI inference, integration, and human oversight combined does not undercut the cost of a research mathematician performing this specialized task. |
| Cost vs. human wage | claude-sonnet-5 | 2/5 | While AI can cut some drafting and coding time, the expert oversight, validation, and iteration needed for trustworthy new methods keeps AI-plus-human costs close to or only modestly below a skilled mathematician's cost. |
| Technical feasibility today | claude-haiku-4-5-20251001 | 2/5 | No deployed product reliably develops original computational methods independently. AI code assistants exist for implementation, but the research and validation phases—including problem framing, method novelty assessment, and proof verification—still require human mathematicians. Tools lack the capability to autonomously produce publishable or industrially-viable new methods. |
| Technical feasibility today | claude-sonnet-5 | 2/5 | AI coding assistants and math-focused LLMs can propose candidate methods or accelerate literature-informed prototyping, but no deployed product reliably originates and validates novel computational methods for real scientific/engineering problems at scale. |
Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
31CI 25–36 · exposure 25 · augmentation 75 · importance 4.1/5 · click for rater detail
Disseminate research by writing reports, publishing papers, or presenting at professional conferences.
31| Dimension | Model | Rating | Rationale |
|---|---|---|---|
| Sector adoption velocity | claude-haiku-4-5-20251001 | 2/5 | Academic and mathematical research communities have adopted AI writing tools for drafting assistance, but adoption remains cautious; publication norms and the high stakes of research integrity slow deep automation in this domain. |
| Sector adoption velocity | claude-sonnet-5 | 3/5 | Academia and research sectors show growing but uneven AI adoption for writing assistance; production-grade autonomous authorship remains rare, with pilots and informal use more common. |
| Augmentation potential | claude-haiku-4-5-20251001 | 4/5 | AI significantly assists mathematicians by generating initial drafts, organizing literature, formatting citations, and suggesting structural improvements—transforming productivity in the writing phase while the mathematician retains full control over content, rigor, and intellectual contribution. |
| Augmentation potential | claude-sonnet-5 | 4/5 | AI substantially aids drafting, editing, formatting, literature summarization, and slide creation, meaningfully boosting researcher productivity while the mathematician retains authorship and judgment. |
| Task automatability | claude-haiku-4-5-20251001 | 2/5 | AI can draft sections of papers and generate report outlines, but mathematical research papers require novel insights, rigorous proof verification, and contextual positioning within the field—tasks demanding deep domain expertise and human judgment that current systems cannot reliably produce end-to-end without substantial human revision. |
| Task automatability | claude-sonnet-5 | 2/5 | AI can draft and edit text, but synthesizing original mathematical research into a coherent paper, choosing framing, and responding to peer review requires human judgment AI cannot yet reliably replace end-to-end.60% of task remains human-driven intellectual work. |
| Adoption barriers | claude-haiku-4-5-20251001 | 4/5 | Research dissemination faces strong barriers: peer review and editorial gatekeeping require human judgment, professional conferences expect live presentation by the researcher, and institutional/funding requirements typically mandate human researcher accountability for published work. |
| Adoption barriers | claude-sonnet-5 | 3/5 | No licensing requirement, but academic norms, authorship attribution, peer review, and reputational stakes create moderate friction against pure AI authorship or presentation. |
| Cost vs. human wage | claude-haiku-4-5-20251001 | 2/5 | AI writing assistance has low inference cost, but the significant human oversight required to verify mathematical correctness, novelty, and fit for publication means total cost remains comparable to or higher than a skilled mathematician writing from scratch. |
| Cost vs. human wage | claude-sonnet-5 | 3/5 | AI drafting tools are cheap relative to a mathematician's time for writing portions, but the overall task still requires substantial expert oversight, keeping total cost comparable rather than drastically cheaper. |
| Technical feasibility today | claude-haiku-4-5-20251001 | 2/5 | While AI tools exist for text generation and formatting, no deployed product reliably produces publication-ready mathematical papers or compelling conference presentations without extensive human editing and verification of technical content. |
| Technical feasibility today | claude-sonnet-5 | 2/5 | LLM writing assistants are used for drafting and polishing text, but no deployed product independently produces publishable mathematical research papers or delivers conference presentations reliably. |
Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
30CI 25–35 · exposure 25 · augmentation 63 · importance 3.8/5 · click for rater detail
Conduct research to extend mathematical knowledge in traditional areas, such as algebra, geometry, probability, and logic.
30| Dimension | Model | Rating | Rationale |
|---|---|---|---|
| Sector adoption velocity | claude-haiku-4-5-20251001 | 2/5 | Despite interest in AI-assisted theorem proving and symbolic computation, academic mathematics departments and research institutions adopt AI tools primarily as assistants to existing researchers rather than as autonomous research agents; replacement or deep displacement remains minimal in practice. |
| Sector adoption velocity | claude-sonnet-5 | 2/5 | Academic mathematics adopts new tools slowly and cautiously; AI-assisted proof exploration is an active research niche but not yet widespread production practice among mathematicians. |
| Augmentation potential | claude-haiku-4-5-20251001 | 3/5 | AI can meaningfully augment mathematicians through proof-checking assistants, computational exploration, literature retrieval, and pattern recognition in large datasets, but the core creative work of formulating novel problems and deriving key insights remains human-centric. |
| Augmentation potential | claude-sonnet-5 | 4/5 | AI tools increasingly help mathematicians explore conjectures, verify proofs, search literature, and perform symbolic computation, meaningfully boosting productivity while humans retain core judgment. |
| Task automatability | claude-haiku-4-5-20251001 | 2/5 | Current AI can assist with computations, proof verification, and literature search, but generating novel mathematical insights, formulating conjectures, and conducting original research in abstract fields requires deep creative reasoning and problem formulation that AI systems cannot reliably perform end-to-end without substantial human direction and validation. |
| Task automatability | claude-sonnet-5 | 2/5 | AI can assist with computations, literature search, and even generate proof ideas, but genuine mathematical research requiring novel conjecture formation, deep insight, and rigorous validation is not reliably automatable end-to-end today.' |
| Adoption barriers | claude-haiku-4-5-20251001 | 4/5 | Conducting publishable mathematical research carries high epistemic and reputational barriers: findings must be peer-reviewed, proofs must be rigorous, and attribution matters deeply in academia, creating strong institutional and professional norms against AI-only authorship of novel mathematical work. |
| Adoption barriers | claude-sonnet-5 | 2/5 | No licensing requirement blocks AI use, but peer review, mathematical community trust, and the need for rigorous proof verification create moderate organizational and epistemic friction. |
| Cost vs. human wage | claude-haiku-4-5-20251001 | 2/5 | AI inference for mathematical tasks is inexpensive, but the integration, validation, and human oversight required to ensure correctness and novelty make the total cost comparable to or potentially exceeding that of a research mathematician's time on the same problem. |
| Cost vs. human wage | claude-sonnet-5 | 2/5 | Current AI systems require significant human oversight and verification for research-level math, so cost savings are limited despite low inference costs; expert validation remains expensive and necessary. |
| Technical feasibility today | claude-haiku-4-5-20251001 | 2/5 | While AI tools can perform symbolic computation and assist with specific subtasks (e.g., Wolfram Alpha, SageMath), no deployed product reliably conducts independent mathematical research or generates publishable new theorems; existing systems require expert supervision and are confined to narrow domains. |
| Technical feasibility today | claude-sonnet-5 | 2/5 | Tools like theorem provers and LLM-based math assistants exist and show promise on benchmark problems, but no deployed product autonomously conducts original mathematical research at scale in production. |
Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
27CI 13–41 · exposure 17 · augmentation 63 · importance 4.3/5 · click for rater detail
Maintain knowledge in the field by reading professional journals, talking with other mathematicians, and attending professional conferences.
27| Dimension | Model | Rating | Rationale |
|---|---|---|---|
| Sector adoption velocity | claude-haiku-4-5-20251001 | 2/5 | While mathematicians use AI tools to aid literature review and summarization, there is minimal evidence of organizations automating or displacing the core task of maintaining professional knowledge—this remains a personal, non-delegable responsibility in academic and research mathematics. |
| Sector adoption velocity | claude-sonnet-5 | 3/5 | Academic and research mathematicians increasingly use AI tools (e.g., summarizers, semantic search like Semantic Scholar) for literature review, though full adoption for 'staying current' remains partial. |
| Augmentation potential | claude-haiku-4-5-20251001 | 3/5 | AI can assist by summarizing papers, identifying relevant citations, and organizing research streams, helping mathematicians process more material faster; however, the irreducible need for deep personal engagement limits how much AI can augment the task. |
| Augmentation potential | claude-sonnet-5 | 4/5 | AI tools significantly help mathematicians efficiently scan, summarize, and discover relevant papers and trends, meaningfully augmenting the reading/research component of staying current. |
| Task automatability | claude-haiku-4-5-20251001 | 1/5 | This task requires active engagement with evolving mathematical discourse, subjective judgment about relevance and depth of understanding, and relationship-building with peers—activities that fundamentally depend on human comprehension, curiosity, and professional judgment that current AI cannot sustain independently. |
| Task automatability | claude-sonnet-5 | 2/5 | AI can help summarize papers and surface relevant literature, but genuinely 'maintaining knowledge' involves ongoing human learning, judgment, networking, and conference attendance that isn't a discrete outsourceable task.dipendenza |
| Adoption barriers | claude-haiku-4-5-20251001 | 4/5 | Professional competence in mathematics fundamentally rests on a mathematician's own direct engagement with the field; institutions, funding bodies, and peers expect original thinkers to maintain first-hand knowledge, creating strong cultural and professional expectations that gatekeep this activity. |
| Adoption barriers | claude-sonnet-5 | 2/5 | No licensing or legal barrier prevents AI assistance here, though the social/professional component (talking with colleagues, conferences) inherently requires human participation. |
| Cost vs. human wage | claude-haiku-4-5-20251001 | 1/5 | The cost of maintaining an AI system to monitor and synthesize mathematical literature continuously, plus human oversight to verify accuracy and relevance, would likely exceed the cost of a mathematician's own reading and professional networking. |
| Cost vs. human wage | claude-sonnet-5 | 3/5 | AI-assisted reading/summarization tools are cheap relative to time spent, but the task also includes human networking and conference attendance that AI cannot substitute for at any cost. |
| Technical feasibility today | claude-haiku-4-5-20251001 | 2/5 | While AI can summarize journal articles and extract key findings from papers, it cannot autonomously maintain coherent, evolving knowledge of a field or engage in genuine peer conversations that drive understanding; any system claiming to do this would be narrow and require constant human validation. |
| Technical feasibility today | claude-sonnet-5 | 2/5 | Products like literature summarization tools and AI research assistants exist and are used informally, but no deployed system autonomously maintains a mathematician's professional knowledge base end-to-end. |
Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
13CI 5–21 · exposure 0 · augmentation 50 · importance 4.1/5 · click for rater detail
Develop new principles and new relationships between existing mathematical principles to advance mathematical science.
13| Dimension | Model | Rating | Rationale |
|---|---|---|---|
| Sector adoption velocity | claude-haiku-4-5-20251001 | 1/5 | Mathematics research remains a human-driven, slow-moving sector with limited digitization of the core creative process. Adoption of AI for novel principle development is negligible; the field still values and relies on individual mathematician insight and peer collaboration. |
| Sector adoption velocity | claude-sonnet-5 | 2/5 | Mathematical research is a small, high-skill academic sector where AI tools are being piloted (e.g., for conjecture generation, proof assistants) but deep production-level adoption for generating new principles remains rare and exploratory. |
| Augmentation potential | claude-haiku-4-5-20251001 | 2/5 | Current AI tools can offer limited assistance by checking calculations, exploring computational patterns, or organizing literature; however, they provide minimal augmentation for the core task of developing genuinely new mathematical principles, which depends on human insight and originality. |
| Augmentation potential | claude-sonnet-5 | 4/5 | AI already meaningfully assists mathematicians by suggesting conjectures, checking proofs, performing symbolic computation, and surfacing relevant literature, substantially speeding up parts of the discovery process even though the core creative leap remains human-driven. |
| Task automatability | claude-haiku-4-5-20251001 | 1/5 | Developing novel mathematical principles and discovering non-obvious relationships requires creative insight, intuition, and deep conceptual understanding that current AI systems cannot reliably achieve. While AI can verify proofs and explore specific conjectures, it cannot independently conceive genuinely new mathematical frameworks or principles at the frontier of the discipline. |
| Task automatability | claude-sonnet-5 | 1/5 | Original mathematical theory development requires deep creative insight and novel conceptualization that current AI cannot reliably produce end-to-end; no system can independently generate new mathematical principles at a level saving 50% of a mathematician's time on this core creative task. |
| Adoption barriers | claude-haiku-4-5-20251001 | 4/5 | Academic and research institutions require human researchers to conduct novel investigations; institutional and peer-review structures demand human authorship and intellectual accountability. The intrinsic requirement for human scientific creativity and judgment creates strong organizational and epistemological barriers. |
| Adoption barriers | claude-sonnet-5 | 2/5 | There is no formal licensing requirement to do mathematical research, but peer review, credentialing within academia, and the need for community validation of new mathematics create moderate institutional friction against pure AI-generated 'discoveries' being credited or trusted. |
| Cost vs. human wage | claude-haiku-4-5-20251001 | 1/5 | The task requires the cognitive investment of highly trained mathematicians (PhDs earning $100k+). Current AI systems offer only narrow assistive capabilities for this specific goal and cannot replace the human effort or cost of developing foundational new mathematics. |
| Cost vs. human wage | claude-sonnet-5 | 2/5 | Since AI cannot reliably perform this task independently, the effective cost of achieving equivalent novel mathematical contributions via AI alone is very high relative to a mathematician, though AI can cheaply assist with sub-components like computation or literature search. |
| Technical feasibility today | claude-haiku-4-5-20251001 | 1/5 | No deployed product reliably performs novel mathematical principle discovery. AI systems can assist with proof verification and pattern-finding in existing domains, but production systems do not independently develop new mathematical relationships or advance mathematical science today. |
| Technical feasibility today | claude-sonnet-5 | 1/5 | No deployed product performs autonomous mathematical theory creation in production; systems like AlphaProof or GPT-based tools remain research-stage demonstrations on narrow problems, not general principle-discovery tools used reliably by working mathematicians. |
Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
7CI 0–15 · exposure 8 · augmentation 38 · importance 2.8/5 · click for rater detail
Design, analyze, and decipher encryption systems designed to transmit military, political, financial, or law-enforcement-related information in code.
7| Dimension | Model | Rating | Rationale |
|---|---|---|---|
| Sector adoption velocity | claude-haiku-4-5-20251001 | 1/5 | Military, law-enforcement, and financial cryptography remain highly specialized, slow-moving sectors with strong institutional preference for human experts and regulatory mandates requiring human sign-off. Adoption of AI-driven cryptanalysis is minimal due to regulatory and security-critical constraints. |
| Sector adoption velocity | claude-sonnet-5 | 2/5 | Government/defense cryptography sectors are historically slow, secretive, and cautious in adopting external AI tools, especially for core classified cryptanalytic work, limiting real-world deployment velocity. |
| Augmentation potential | claude-haiku-4-5-20251001 | 2/5 | AI can assist mathematicians with literature searches, computation of known attacks, and verification of implementation details, but augmentation is limited because the core task—designing novel secure systems or breaking ciphers—requires human insight and cannot be meaningfully delegated to assistive AI without human verification of every step. |
| Augmentation potential | claude-sonnet-5 | 3/5 | AI can meaningfully assist with mathematical exploration, pattern detection, code generation, and literature review, augmenting a human cryptographer's productivity even though it cannot replace core judgment. |
| Task automatability | claude-haiku-4-5-20251001 | 1/5 | Encryption system design, analysis, and decipherment require deep mathematical insight, novel problem-formulation, and creative breakthroughs that current AI cannot perform end-to-end. While AI can assist with implementation details or pattern recognition, the core work of designing secure systems and breaking ciphers demands human mathematical reasoning and novel algorithmic contributions. |
| Task automatability | claude-sonnet-5 | 2/5 | Designing and analyzing cryptographic systems requires deep theoretical rigor, novel proofs, and adversarial creativity that current AI cannot reliably perform end-to-end; AI can assist with subcomponents (code implementation, literature search) but not the core cryptanalytic/design task at equal quality. |
| Adoption barriers | claude-haiku-4-5-20251001 | 5/5 | This task is deeply regulated: encryption design and cryptanalysis for military, political, and law-enforcement purposes are subject to strict licensing, export controls (EAR, ITAR), and requirements that certified humans design and validate systems. Legal liability for cryptographic failure is severe, and security clearances are typically mandatory. |
| Adoption barriers | claude-sonnet-5 | 5/5 | This work typically involves security clearances, government authorization, and strict human sign-off due to national security and legal implications, creating hard institutional and regulatory barriers to automation. |
| Cost vs. human wage | claude-haiku-4-5-20251001 | 1/5 | The task involves high-value intellectual property and security-critical work where human cryptographers command significant salaries. AI inference and integration costs would be minimal compared to the sunk cost of human expertise and the liability of algorithmic failure in a security-critical domain. |
| Cost vs. human wage | claude-sonnet-5 | 2/5 | Given the low reliability and high stakes of getting cryptography wrong, AI assistance requires extensive expert oversight, making all-in cost not dramatically cheaper than skilled human cryptographers for this specialized task. |
| Technical feasibility today | claude-haiku-4-5-20251001 | 1/5 | No deployed AI system reliably designs cryptographic systems or deciphers novel encryption schemes. AI can help analyze known attacks or suggest optimizations, but production systems for cryptanalysis and cipher design require human cryptographers making high-stakes security decisions. |
| Technical feasibility today | claude-sonnet-5 | 1/5 | No deployed product autonomously designs or deciphers cryptographic systems used in classified military/financial contexts; this remains a research-stage capability with occasional narrow benchmark successes on toy ciphers. |
Related occupations — Computer & Mathematical
How to read this
A high substitution score does not mean this job disappears — it means a large share of its current tasks face replacement pressure, so the mix of tasks is likely to change. High augmentation alongside substitution typically means the occupation reorganizes around the protected tasks. Wide confidence intervals mean the rater panel disagreed: treat those scores as open questions, not verdicts.
What would change this score
New model capabilities (automatability, feasibility), falling inference costs (cost ratio), regulation and licensing shifts (barriers), and measured sector adoption (velocity) all re-enter at every index release. Each release is recomputed, versioned and kept queryable — scores are claims with a date on them, not permanent labels.