Lean Engineer - Formal Mathematics

Mercor; San Francisco (CA); Hybrid; GBP 94,000 - 115,000; Part time

Job summary

Mercor seeks a Lean Engineer to advance formal mathematics using Lean 4 and mathlib in a remote, contract role. You will craft correct proofs, translate problems into formal statements, and review AI-generated Lean content for accuracy.

Applicants should have hands-on Lean 4 experience, comfort with mathlib tactics, and a strong proof-based math or logic background, with a commitment of 20–40 hours per week during weekdays.

Qualifications

• Hands-on experience writing formal proofs in Lean 4.
• Comfort with mathlib and Lean 4 tactics.
• Strong background in proof-based mathematics, theory CS, or logic.
• Ability to turn a written statement and proof into a formal statement and proof.
• Engage reliably for at least 20 hours/week during weekdays.
• Clear written communication and ability to explain proof strategy precisely.

Responsibilities

• Write Lean 4 statements and proofs that compile against mathlib.
• Formalize natural-language mathematics from problems to lemmas.
• Review AI-generated Lean statements and proofs with feedback.
• Help define guidelines for proof quality and mathlib conventions.
• Collaborate with Lean engineers to maintain standards.

Skills

Lean 4

Mathlib

Theorem Proving

Coq/Rocq

Haskell

Education

Degree in mathematics or theoretical CS

Tools

Lean 4 metaprogramming

AI-for-math tooling

Job description

About the job

Mercor connects elite creative and technical talent with leading AI research labs. Headquartered in San Francisco, our investors include Benchmark, General Catalyst, Peter Thiel, Adam D'Angelo, Larry Summers, and Jack Dorsey.

Position: Lean Engineer, Formal Mathematics (Lean 4, Mathlib, Theorem Proving)
Type: Contract
Compensation: $90–$110/hour
Location: Remote
Commitment: 20–40 hours/week

Role Responsibilities

• Write correct, idiomatic Lean 4 statements and proofs that compile against current mathlib. Cover areas such as algebra, analysis, number theory, combinatorics, and logic.
• Formalize natural-language mathematics from competition problems and textbook results to research-level lemmas. Ensure the formal statement matches the original.
• Review AI-generated Lean statements and proofs. Identify failures or incorrect proofs and provide 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 maintain consistent standards and elevate quality.

Qualifications

Must-Have

• Hands-on experience writing formal proofs in Lean 4. Examples include mathlib contributions, a formalization project, or a Lean library or tool.
• Comfort with mathlib and Lean 4 tactics. Ability to find and use the right lemmas.
• Strong background in proof-based mathematics, theoretical computer science, or logic through a degree or research record.
• Ability to turn a written statement and proof into a correct formal statement and a proof that checks.
• Engage reliably for at least 20 hours/week during weekdays.
• Clear written communication and ability to explain proof strategy and formalization choices precisely.

Preferred

• Experience with other proof assistants or dependently typed languages (Coq/Rocq, Isabelle, Agda, Haskell).
• Experience with Lean metaprogramming or AI-for-math work such as LLM provers, Lean agent environments, or benchmarks like miniF2F, ProofNet, or PutnamBench.

Compensation & Legal

• W-2 employment with Cincinnatus LLC.
• Equal Employment Opportunity employer.