Applied Mathematics — P5

RDSCIE.APPLIEDME156.P5

P5P5 — Expert Professionalhigh0.90approvedglobalv1

Applied Mathematics — develops and applies mathematical models, numerical algorithms, optimization, and statistical/computational methods (on HPC/GPU architectures) to solve scientific and mission-driven problems. Distinct from sibling Data Science/ML focuses (which center on data products and learned models) and from pure Computational/Statistics focuses: this focus is anchored in formulating real-world problems as mathematical models and designing/analyzing the numerical methods that solve them at scale.

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Level

P5 · P5 — Expert Professional · 8–12 yrs

Function · Focus

R&D Science & Engineering · Applied Mathematics

Market pay (median)

$138k ($109k–$176k)

Pay basis

function-anchored · wide bars

Focus — Applied Mathematics

Material SKILL differential vs the function baseline.

Responsibilities by level

What this person actually does at each level on the professional track — escalating scope, not one generic blob. Your level is highlighted.

Develops and applies mathematical and computational techniques — analytic and statistical modeling, numerical analysis, signal processing, and computer simulations — for scientific and mission applications under general instruction.
Conducts self-initiated research within defined problem boundaries and maintains awareness of the relevant technical literature.
Effectively uses available computing architectures including high-performance computing (HPC) systems to run scientific models, building simulation/modeling software in at least one language (e.g., Python, C++, Julia, Fortran).
Independently owns features or well-scoped projects end-to-end and publishes results in peer-reviewed journals or presents at conferences.
Works as part of interdisciplinary teams to deliver mission-oriented results on externally driven timelines, beginning to mentor junior staff.

Develops and applies mathematical models, numerical algorithms, and optimization or statistical methods across a diverse set of problems with day-to-day independence, planning own work to milestone review.
Conducts analytic and statistical modeling, numerical analysis, and large-scale computer simulations on HPC/GPU-accelerated systems, evaluating identifiable factors to select among methods.
Carries out self-initiated research, publishes in peer-reviewed venues, and integrates machine learning methods into numerical methods and simulations where appropriate.
Coordinates project activities and collaborates with experimentalists, theorists, and computer scientists, networking with senior professionals across departments.
Mentors junior mathematicians and reviews their analyses and research software contributions.

Provides technical leadership and oversight of complex research tasks, performing in-depth analysis of complex variables across the modeling-to-numerical-solution pipeline.
Initiates and leads scientific and technical research projects, selecting methods and approaches with functional impact and coordinating across groups.
Serves as a subject-matter expert in a specific applied-mathematics area (e.g., optimization, numerical PDEs, statistical modeling, HPC-scalable algorithms).
Oversees level-one and level-two scientists, setting technical standards for portable, high-performance, sustainable research software.
Contributes to securing competitive funding through proposals and influences research and design decisions on mission deliverables.

P5this profile

Acts independently on broad and strategic applied-mathematics assignments that contribute to company objectives, working with intangibles and high independence.
Sets technical direction and standards for a domain, leading interdisciplinary research teams and supervising scientists on special tasks.
Secures competitive funding via research grants and sponsored projects, often from government agencies such as DOE or DOD, owning the program and stakeholder relationships.
Serves as an external spokesperson and builds influential networks across the scientific community, representing the organization's applied-mathematics capability.
Drives high-impact technical decisions as a recognized authority, bridging data, systems, and decision-makers.

Provides high-level scientific leadership and oversight of multiple research projects, shaping strategy across product areas or the organization.
Generates and carries out undirected research programs with wide latitude for un-reviewed action and decision, defining the problems worth solving.
Coordinates and supervises technical staff of all levels and oversees senior scientists, multiplying capability through mentorship and influence.
Acts as a recognized thought leader who shapes the field's applied-mathematics methods (numerical algorithms, optimization, HPC-scale simulation), influencing both industry and company direction.
Owns major funding portfolios and partnerships, aligning research programs with long-term organizational objectives.

Sets direction for applied-mathematics functions and industry initiatives, anticipating emerging challenges and defining long-term research roadmaps that impact company-wide strategy.
Develops new theories, models, or numerical technologies and solves ambiguous, precedent-free problems with broad business and industry consequences.
Operates with complete independence, driving undirected, field-defining research programs and establishing the technical agenda others follow.
Networks with executives, agency program managers, and industry leaders, persuading and educating senior stakeholders on strategic scientific priorities and major funding directions.
Provides high-level mentorship to senior and principal scientists, shaping company-wide applied-mathematics capability through publications, patents, and recognized contributions rather than direct authority.

Level guidelines

The universal leveling rubric applied to this function — how scope, complexity, collaboration, and experience step up across levels.

Level	Knowledge & Application	Complexity & Problem Solving	Collaboration & Interaction	Typical Degree & Years
P2	Applies conventional mathematical modeling, numerical analysis, and statistical methods to moderate-scope problems; uses at least one programming language and HPC systems with general instruction.	Exercises moderate judgment in familiar contexts; problems are well-bounded with defined procedures and individual-deliverable scope.	Builds productive project relationships within interdisciplinary teams; communicates results to immediate collaborators.	2+ years with a BA/BS, or an MS/PhD with no prior experience (including postdoc/entry tier capable of an independent research program).
P3	Applies a range of computational mathematics, optimization, and statistical-modeling techniques across diverse problems; runs models on HPC/GPU systems and integrates ML where useful.	Evaluates identifiable factors to select methods; works with day-to-day independence and plans own work to milestone review.	Networks with senior professionals and across departments; may coordinate project activities and mentor juniors.	5+ years (BA), 3 years (MA), or a PhD without additional experience.
P4	Deep expertise in a specific applied-mathematics domain; performs in-depth analysis of complex variables and sets standards for sustainable research software.	Solves complex issues with functional impact; selects methods and approaches and may lead teams through technical ambiguity.	Coordinates across groups, influences research and design decisions, and oversees level-one and level-two scientists.	8+ years, often with graduate education; recognized subject-matter expert within the company.
P5	Extensive expertise applied to strategic, broad, or unique assignments; brings barriers-to-entry depth in numerical algorithms, optimization, or HPC-scale modeling.	Works on strategic issues involving intangibles with high independence; defines approaches for novel mission problems.	Builds influential networks, serves as external spokesperson, and supervises scientists on special tasks; owns funding and stakeholder relationships.	12+ years with extensive expertise; established funding track record (grants/sponsored research).
P6	Field-shaping mastery of applied mathematics; defines methods and standards used organization-wide and within the discipline.	Visionary, field-shaping problem-solving; generates undirected research programs with full independence and wide latitude for un-reviewed decisions.	Influences industry and company as a recognized thought leader; provides high-level mentorship and coordinates staff of all levels.	15+ years as a principal expert; often PhD plus industry leadership and a major funding portfolio.
P7	Develops new theories, models, and numerical technologies that advance the field and impact company-wide strategy; sets long-term technical roadmaps.	Solves ambiguous, precedent-free problems with broad business and industry consequences; anticipates emerging challenges and defines direction.	Networks with executives, agency program managers, regulators, and industry leaders; persuades and educates senior stakeholders and mentors senior professionals.	20+ years or equivalent recognition, often PhD with significant industry contributions, patents, or publications.

Skills

Focus-specific skills the role applies — the relevance layer beyond the occupational base.

Mathematical modeling: Develops scientific or mathematical models to formulate and solve practical, real-world problems.
Computational mathematics: Applies computational methods and develops new numerical algorithms for optimization, linear algebra, data analysis, and statistical models.
Numerical analysis: Analyzes and designs numerical methods and algorithms for large-scale scientific and engineering problems.
Optimization: Develops and applies optimization algorithms to solve scientific and engineering problems.
Statistical modeling: Conducts analytic and statistical modeling and data analysis to identify trends or relationships among variables.
High-performance computing: Develops, improves, and runs scientific models on HPC and GPU-accelerated systems.
Programming: Runs data analytics and builds simulation/modeling software in at least one programming language.
Scientific software development: Builds portable, high-performance, sustainable research software, including object-oriented programming for data analysis.
Machine learning: Integrates machine learning methods into numerical methods and large-scale simulations.
Communication: Explains results clearly to non-technical people and bridges data, systems, and decision-makers.
Collaboration and leadership: Works cooperatively with project managers, experimentalists, theorists, applied mathematicians, and computer scientists.
Funding acquisition: Seeks clients and competitive funding for research, often from government agencies such as DOE or DOD.

Provenance

The evidence base behind this profile — every layer is sourced; quality is scored by an adversarial review panel (1–5; passes at ≥4 on the minimum dimension).

Level differentiation5.0Focus specificity5.0Concreteness4.5Factual accuracy5.0Real-world coverage4.5

10 sources

Level — P5 — Expert Professional

Expert in field; key problem solver and project leader, authority in multiple areas

Scope: Multiple systems or a technical domain
Autonomy: Sets direction within the domain
Complexity: Novel, high-ambiguity problems; establishes the approach
Impact: Org / multi-team outcomes
Decision rights: Authority over a technical domain
Leadership: Leads cross-team technical initiatives
Typical experience: 8–12 yrs

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