Domain Expert: Mathematics

Design rigorous mathematical tasks to evaluate AI performance in computation.

About Turing:

Turing’s mission is to accelerate superintelligence to drive real economic progress. Headquartered in San Francisco, Turing works with frontier AI labs to generate high-quality data, evaluations, and reinforcement learning environments that improve model capabilities in coding, reasoning, tool use, and multimodality. In coding, Turing is the largest and longest-running data provider in the category. Turing also works with Fortune 500 enterprises across Financial Services, Life Sciences, Healthcare, Retail, Automotive, and CPG to build and deploy end-to-end agentic AI systems inside mission-critical workflows. By operating on both sides, Turing closes the loop between frontier research and enterprise deployment, turning real-world deployment signals into better data, evaluations, and more capable models.

Role Overview

We are seeking Mathematics experts to contribute advanced mathematical expertise to task design, data curation, and evaluation for frontier AI models and labs. This role focuses on developing rigorous mathematical tasks, reviewing complex solutions, and advising client teams assessing AI-generated outputs.

You will design tasks that evaluate whether AI agents can perform authentic mathematical work in a computational environment: inspecting files, writing and running code, using mathematical software, debugging workflows, analyzing data, and producing verifiable artifacts such as proofs, numerical solutions, computational notebooks, and reproducible analyses.

The role is designed for experienced researchers, faculty, and industry specialists interested in improving the accuracy, reasoning, and reliability of AI systems in mathematics.

What You’ll Do Day-to-Day

• Design mathematically rigorous tasks with clear objectives, appropriate inputs, and verifiable outcomes.
• Develop computational workflows that require AI agents to use mathematical software, write code, and produce reproducible results.
• Lead expert review of complex or ambiguous mathematical problems and AI-generated solutions.
• Review content within your areas of expertise, such as algebra, analysis, geometry, topology, number theory, probability, combinatorics, optimization, or numerical methods.
• Evaluate proofs, derivations, algorithms, and computational results for correctness and completeness.
• Identify invalid assumptions, logical gaps, unsupported conclusions, and numerical errors.
• Assess convergence, stability, approximation error, and computational efficiency where relevant.
• Develop evaluation frameworks, scoring rubrics, reference solutions, and automated checks where appropriate.
• Facilitate structured resolution of mathematical disagreements among reviewers.
• Provide expert guidance to client teams and clearly document evaluation decisions.

Requirements

• PhD in Mathematics, Applied Mathematics, or a closely related discipline.
• Minimum three years of post-PhD research, teaching, or relevant industry experience.
• Current or recent experience in academic research, an industrial R&D environment, or a recognized research institution.
• Strong understanding of mathematical reasoning, proof techniques, and analytical methods relevant to your specialization.
• Specialized expertise in one or more areas of pure or applied mathematics.
• Experience using computational tools or programming languages, such as Python, Julia, MATLAB, Mathematica, SageMath, or equivalent platforms.
• Ability to design mathematical problems with clear assumptions, well-defined constraints, and independently verifiable solutions.
• Demonstrated research contributions through peer-reviewed publications or substantial mathematical and computational projects.
• Ability to critically assess proofs, algorithms, numerical methods, and interpretations of computational results.
• Strong written communication skills and the ability to explain mathematical reasoning clearly.
• Ability to lead and document technical consensus.
• Disciplined adherence to project protocols, confidentiality requirements, and quality standards.

Preferred Qualifications

• Faculty appointment at the rank of Assistant Professor or above, or equivalent senior research or industry experience.
• Prior experience with AI evaluation, mathematical benchmark development, automated reasoning, or formal verification.
• Experience with proof assistants such as Lean, Coq, or Isabelle.
• Experience developing reproducible computational notebooks, reference implementations, or automated validation workflows.
• Experience reviewing journal articles, research proposals, or technical reports.
• Experience teaching or mentoring graduate students, researchers, or technical teams.
• Active involvement in professional societies such as AMS, SIAM, MAA, or relevant specialist organizations.

Performance Expectations

• Take ownership of assigned task-design and review batches.
• Deliver mathematically sound tasks, reference solutions, and evaluations.
• Ensure computational artifacts are reproducible and can be independently verified.
• Clearly document assumptions, proof steps, computational dependencies, and limitations.
• Distinguish rigorous proofs from numerical evidence, heuristic arguments, and conjectures.
• Maintain consistency and reliability when collaborating with other expert reviewers.
• Communicate constructively with client teams during advisory discussions.
• Meet agreed deadlines and follow established evaluation protocols.
• Disclose relevant equity, advisory, consulting, or employment relationships with organizations whose technologies or products may appear in project content.
• Disclosed conflicts do not automatically disqualify applicants but may influence assignment allocation.

Perks of Freelancing with Turing

• Flexible, fully remote collaboration.
• Learn how advanced AI systems are trained and evaluated.
• Contribute to projects with leading AI and LLM companies.
• Apply your mathematical expertise to challenging, real-world AI evaluation problems.
• Collaborate with experts across disciplines and geographies.
• Potential for contract extension based on project needs and performance.

Engagement Details

• Engagement type: Independent contractor.
• Anticipated commitment: An average of 15 hours per week, with up to 40 hours per week during peak periods.
• Duration: Four weeks.
• Timeline and assignments depend on project requirements.
• Fully remote and asynchronous, with occasional synchronous calls.
• NDA required upon engagement; detailed scope of work shared after NDA execution.

Evaluation Process

• Submit your CV, including academic appointments or relevant research and industry experience.
• Include two recent peer-reviewed publications or equivalent mathematical or computational contributions.
• Provide a brief statement of interest, approximately 300 words, describing your experience with mathematical problem design, computational workflows, structured technical writing, or AI evaluation.
• Applicants will be shortlisted based on qualifications and relevant domain expertise.
• Shortlisted applicants will participate in one interview.
• Successful applicants will complete a brief calibration assignment before full engagement.

Skills: PhD Maths