Lean Engineer, Formal Mathematics (Lean 4, Mathlib, Theorem Proving)

AI Trainer Jobs; United States; Remote; USD 65,000 - 95,000; Part time

Job summary

Cincinnatus LLC is seeking Lean engineers and formal mathematicians to help its AI lab state and prove mathematics in Lean 4. You will write and review Lean proofs, formalize statements from informal math, and provide precise feedback on AI-generated proofs. Part-time commitment of 20–40 hours per week with potential to increase.

The role involves collaborating with researchers to ensure fidelity, contribute to proof quality guidelines, and work with mathlib across multiple areas of mathematics.

Qualifications

• Hands-on experience writing formal proofs in Lean 4, including mathlib contributions or formalization projects.
• Ability to turn informal mathematics into correct formal statements and proofs.
• Strong background in proof-based mathematics or logic.
• Availability for at least 20 hours/week on weekdays.
• Clear written communication of proof strategy and formalization choices.

Responsibilities

• Write Lean 4 statements and proofs that compile against current mathlib across algebra, analysis, number theory, combinatorics and logic.
• Formalize natural-language mathematics, from problems to lemmas, ensuring fidelity to the original statement.
• Review AI-generated Lean statements and proofs, identifying gaps and providing precise feedback.
• Help define guidelines and rubrics for proof quality and mathlib conventions.
• Collaborate with Lean engineers and researchers to maintain high standards.

Skills

Lean 4 proofs

Formal mathematics

Proof strategy

Education

Degree in mathematics or logic

Tools

Lean 4

mathlib

Coq

Isabelle

Lean metaprogramming

Job description

Help a leading AI lab teach its models to write real, machine-checked mathematics in Lean.

Overview

A leading AI lab is looking for Lean engineers, formal mathematicians and proof engineers to help its AI models state and prove mathematics correctly. You'll write and review Lean 4 proofs, turn informal math into precise formal statements, and help the lab's researchers judge whether a model's proof is not just accepted by the checker but actually proves the right thing. If you enjoy writing Lean, know your way around mathlib, and can explain why a formalization is faithful or subtly wrong, this role is for you. This is a part-time commitment of at least 20 hours per week, with the option to increase to up to 40 hours per week.

This is a W-2 employment position with Cincinnatus LLC (or appropriate international entity), with the opportunity to be placed at a leading AI lab as part of their extended workforce.

Key Responsibilities

Write correct, idiomatic Lean 4 statements and proofs that compile against current mathlib, across areas such as algebra, analysis, number theory, combinatorics and logic.

Formalize natural-language mathematics, from competition problems and textbook results to research-level lemmas, paying close attention to whether the formal statement matches the original.

Review AI-generated Lean statements and proofs, find where they fail or prove the wrong thing, and give clear, specific written feedback.

Help define guidelines and rubrics for proof quality, statement fidelity and mathlib conventions.

Collaborate with other Lean engineers and the lab's researchers to keep standards consistent and keep raising the quality bar.

Core Qualifications

Hands-on experience writing formal proofs in Lean 4, for example mathlib contributions, a formalization project, a Lean library or tool, or autoformalization work.

Comfort with mathlib and Lean 4 tactics, and with finding and using the right lemmas.

A strong background in proof-based mathematics, theoretical computer science or logic, through a degree or a research record.

The ability to turn a written statement and proof into a correct formal statement and a proof that checks.

Ability to engage reliably for at least 20 hours/week during weekdays.

Clear written communication and the ability to explain proof strategy and formalization choices precisely.

Nice to have: experience with other proof assistants or dependently typed languages (Coq/Rocq, Isabelle, Agda, Haskell), Lean metaprogramming, or AI-for-math work such as LLM provers, Lean agent environments, or benchmarks like miniF2F, ProofNet or PutnamBench. You don't need all of these to apply.

About Cincinnatus LLC: Cincinnatus LLC is an enterprise staffing company that partners with leading technology companies to source and employ highly skilled professionals for contingent and contract-based opportunities. Cincinnatus serves as the employer of record for these engagements, providing W-2 employment, payroll, benefits, and compliance, while placing employees directly within client teams to work on high-impact initiatives.

Equal Employment Opportunity: Cincinnatus is proud to be an Equal Employment Opportunity employer. We do not discriminate based upon race, religion, color, national origin, sex (including pregnancy, childbirth, reproductive health decisions, or related medical conditions), sexual orientation, gender identity, gender expression, age, status as a protected veteran, status as an individual with a disability, genetic information, political views or activity, or any other legally protected characteristic.

We consider all qualified applicants without regard to legally protected characteristics and provide reasonable accommodations upon request.