Formal Mathematician - Fully Remote

Mercor; Greater London; Hybrid; GBP 40,000 - 80,000; Part time

Job summary

Cincinnatus LLC is seeking Lean engineers and formal mathematicians to help an AI lab state and prove mathematics in Lean 4. You will write proofs, translate informal math to formal statements, and evaluate model proofs for fidelity.

The role is part-time (≥20 hours/week, up to 40 hours) and employed via W-2 with Cincinnatus LLC, with placement at a leading AI lab within the extended workforce.

Qualifications

• Hands-on experience writing formal proofs in Lean 4 or related tools.
• Ability to translate informal math to formal Lean statements and proofs.
• Proven ability to review AI-generated Lean content and provide precise feedback.

Responsibilities

• Write correct Lean 4 statements and proofs compatible with mathlib.
• Formalize natural-language mathematics and compare with original statements.
• Review AI-generated Lean content and provide clear feedback.
• Help define proof-quality guidelines and rubrics.
• Collaborate to raise the overall proof quality standards.

Skills

Lean 4

Formal proofs

Mathlib familiarity

Proof engineering

Written communication

20+ hrs/week commitment

Education

Bachelor's or higher in Mathematics/CS/Logic

Tools

Lean tactics

Coq/Rocq/Isabelle (nice to have)

Lean metaprogramming (nice to have)

Job description

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

1. 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.

2. 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.

3. 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.

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.