Remote | Computational Mathematician (Scientific Computing) — Up to $60/hour

We are sharing a specialised part-time consulting opportunity for PhD-level applied mathematicians with strong expertise in scientific computing, numerical methods, computational modelling, and research-grade programming.

This role focuses on designing original, executable research problems based on authentic mathematical and computational workflows. Selected experts will create challenging coding-based problems across numerical linear algebra, computational mechanics, and computational finance, develop rigorous reference solutions and grading criteria, and refine tasks through systematic testing.

Key Responsibilities

Applied Mathematics Problem Design

• Develop original research-level computational mathematics problems
• Build tasks from published papers, public datasets, open-source repositories, or independently designed scenarios
• Create problems requiring multi-step mathematical and computational reasoning
• Ensure tasks reflect realistic scientific or quantitative workflows rather than standard textbook exercises
• Design problems with precise, reproducible, and mathematically defensible solutions

Numerical Linear Algebra

• Develop computational tasks involving matrix methods, numerical solvers, decompositions, and large-scale linear systems
• Design problems requiring careful consideration of numerical stability, conditioning, convergence, and computational efficiency
• Evaluate alternative numerical approaches and their limitations
• Incorporate realistic edge cases and failure modes
• Validate numerical results using reproducible code

Computational Mechanics

• Create mathematical modelling and simulation tasks involving mechanics where relevant
• Develop problems requiring numerical treatment of physical systems, discretisation, or equation solving
• Evaluate modelling assumptions, boundary conditions, and computational accuracy
• Design tasks requiring interpretation of numerical simulation results
• Ensure mathematical formulations remain consistent with the underlying physical problem

Computational Finance

• Develop quantitative tasks involving financial modelling and numerical methods
• Create scenarios requiring simulation, optimisation, pricing, or quantitative risk analysis
• Evaluate assumptions and numerical methods used in financial computations
• Design problems where correct conclusions depend on both mathematical rigour and computational implementation
• Validate outputs against authoritative reference calculations

Scientific Programming

• Write and validate computational workflows using Python or R
• Develop numerical implementations, reference calculations, and solution validators
• Debug scientific code and identify implementation or numerical errors
• Build reproducible workflows suitable for automated testing
• Ensure code accurately implements the underlying mathematical specification

Reference Solutions & Grading Criteria

• Produce authoritative reference solutions and supporting calculations
• Define clear criteria for determining whether a solution is correct
• Identify essential mathematical reasoning, computational steps, and numerical outputs
• Develop grading logic capable of distinguishing correct solutions from plausible but flawed approaches
• Ensure evaluation standards remain precise and consistently applicable

Testing & Difficulty Calibration

• Test tasks against advanced computational systems
• Analyse failure modes and identify where reasoning or implementation breaks down
• Refine prompts, inputs, constraints, and expected outputs based on testing
• Adjust problem difficulty while preserving mathematical validity
• Finalise tasks only when they reliably require advanced quantitative and computational expertise

Research Engineering Workflow

• Work through a Git/GitHub pull-request workflow
• Run and validate code in Docker-based environments
• Respond to automated quality checks and reviewer feedback
• Maintain clean, reproducible code and supporting documentation
• Collaborate effectively within structured scientific software workflows

Ideal Profile

• PhD required in Mathematics, Applied Mathematics, Computational Mathematics, or a closely related field
• Demonstrated depth in at least two of the following:
  • Numerical linear algebra
  • Computational mechanics
  • Computational finance
• Strong working proficiency in Python or R
• Hands-on experience using programming for mathematical modelling, numerical analysis, simulation, or quantitative research
• Comfortable with Git/GitHub
• Experience running code in Docker or other containerised environments
• Strong understanding of numerical accuracy, computational reproducibility, and scientific validation
• Ability to translate advanced mathematical concepts into clearly defined computational problems
• Peer-reviewed publications are advantageous
• Prior scientific software or research engineering experience is highly valued
• Strong written communication and ability to document mathematical assumptions, methods, and solutions precisely

Engagement Details

• Part-time independent contractor engagement
• Fully remote
• 20+ hours per week
• Initial duration of approximately 6 weeks
• Immediate start
• Compensation: Up to $60/hour
• Work includes computational problem design, scientific coding, reference-solution development, grading criteria, testing, and task refinement
• Projects may be extended, shortened, or concluded based on project needs and performance
• Work must be completed without using confidential or proprietary information belonging to any employer, client, institution, or other third party
• H1-B and STEM OPT support is unavailable for this engagement

About the Platform

This opportunity is available through 24-MAG LLC. We connect experienced professionals with remote consulting opportunities across technical, evaluation, and project-based workstreams.

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