Pure Mathematics Specialist – Freelance AI Trainer Project

Agency; United States; Remote; USD 48,000 - 90,000; Full time

Benefits offered by this job

Remote freelance contract

Job summary

Agency is seeking a Pure Mathematics and Lean 4 Specialist for a freelance AI trainer project. The role emphasizes rigorous proof construction, formalization in Lean 4, and collaboration to improve evaluation benchmarks.

Ideal candidates hold a PhD or PostDoc in pure mathematics and bring deep knowledge in probability, analysis, algebra, and category theory, with strong metacognitive communication skills.

Qualifications

• PhD or PostDoc in pure mathematics is required.
• Deep foundations in probability, measure theory, real/functional analysis, optimization, abstract algebra, and category theory.
• Fluency in Lean 4 with ability to express proofs in Lean syntax.

Responsibilities

• Construct and evaluate complex proofs and verify rigor, identifying subtle errors.
• Translate mathematical material into Lean 4 code for implementation and evaluation.
• Collaborate to refine prompts, evaluation frameworks, and mathematical reasoning benchmarks.

Skills

Pure mathematics

Proof writing

Metacognitive communication

Probability theory

Education

PhD or PostDoc in pure mathematics

Tools

Lean 4

Job description

Are you a theoretical mathematics expert eager to shape the future of AI? Large-scale language models are rapidly advancing, and their ability to handle rigorous proof-based reasoning depends on high-quality mathematical training data. With your advanced expertise, tomorrow’s AI can better understand abstraction, logic, measure theory, homotopy, and the deep structures of modern mathematics. That training data begins with you - your insight will help power the next generation of AI.

We’re looking for specialists with deep foundations in pure mathematics who can engage with advanced topics across probability theory, measure theory, real and functional analysis, optimization, abstract algebra, and category theory. Coupled with this deep foundation, we need each expert to have a normalized fluency in Lean 4, the proof assistant and programming language.

On a typical day, you will construct and evaluate complex proofs, substantiate the mathematical reasoning for correctness and rigor while identifying subtle conceptual or logical failures, and translate this material to successfully build in .lean syntax. You will also collaborate with our team to refine prompts, evaluation frameworks, and mathematical reasoning benchmarks, enhancing the overall quality of our operations.

Candidates fluent in Lean 4 with an in-progress or freshly earned PhD or current PostDoc experience in pure mathematics are ideal. A strong command of core areas is required, and applicants should be comfortable with topics such as Markov’s and Chebyshev’s inequalities, Hoeffding bounds, convergence theorems, the Carathéodory extension theorem, the Riesz representation theorem, Banach–Alaoglu, Lax–Milgram, stochastic approximation, Van Kampen’s theorem, the Yoneda embedding, and representability in cohomology.

Clear, metacognitive communication (explicitly articulating reasoning and proof strategies) is essential.

Ready to turn your Lean 4 fluidity and pure math expertise into the reasoning backbone of tomorrow’s AI?

We offer a pay range of $35 to $65 per hour, with the exact rate determined after evaluating your experience, expertise, and geographic location. Final offer amounts may vary from the pay range listed above.

As a contractor, you’ll supply a secure computer and high-speed internet; company-sponsored benefits such as health insurance and PTO do not apply.

Job title: Pure Mathematics and Lean 4 Specialist – Freelance AI Trainer Project

Employment type: Contract

Workplace type: Remote