Lean 4 Proof Engineer - Mathematical Formalization

Montreal, Quebec, Canada
Remote
Posted Oct 8, 2026
1 position

US$170–US$200 / hour

Opens LinkedIn

Employment type: Contract
Experience level: Mid-level · 2+ years
Minimum education: Master’s degree
Posting language: English
Working hours: 40 hours per week
Location requirements: Country, Montreal, Quebec, Canada
Seniority: Entry level

Job summary

Translate informal mathematical arguments into clear, correct, machine-verifiable Lean 4 proofs, and identify assumptions, gaps, and structures that can be formalized. Work with AI researchers to evaluate formal verification strategies, investigate automated prover failures, and advise on proof decomposition and readable proof scripts.

Job details

Lean 4 Proof Engineer — Mathematical Formalization About The Role What if your deep mathematical training could directly shape how the world's most advanced AI systems reason, prove, and think? We're looking for Lean 4 Proof Engineers to translate rigorous mathematical arguments into machine-verifiable formalizations — working at the very frontier of what proof assistants can express and automate. This is a fully remote, flexible contract role built for mathematicians who find beauty in precision and satisfaction in resolving the gaps that automated tools cannot yet bridge. Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: 10–40 hours/week What You'll Do Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility Analyze domain-specific and general proofs to identify hidden assumptions, gaps, and formalizable sub-structures Construct formalizations that test the limits of existing proof assistants — especially where automated tools struggle or fail entirely Collaborate with AI researchers to design, refine, and evaluate strategies for advancing formal verification pipelines Investigate breakdown points in automated provers and articulate why they occur — missing lemmas, complexity barriers, insufficient libraries Develop highly readable proof scripts aligned with mathematical best practices and proof assistant idioms Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models Formalize classical proofs and compare machine-verifiable structures against their textbook counterparts Who You Are Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field Have a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics Possess hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof systems — Lean 4 strongly preferred Are deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics Can take a dense, informal argument and express it precisely in a form a machine can verify Nice to Have Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools Experience contributing to large-scale formalization projects such as Mathlib Exposure to theorem provers where automated reasoning frequently fails or requires extensive manual scaffolding Prior experience with data annotation, evaluation systems, or AI training workflows Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies to non-specialist collaborators Why Join Us Work on genuinely frontier problems alongside world-leading AI research teams and labs Fully remote and flexible — structure your work around your life, not the other way around Freelance autonomy with the substance of meaningful, intellectually demanding work Gain direct exposure to how cutting-edge large language models are trained and evaluated Contribute to mapping the boundary of what formal verification can express and automate Potential for ongoing work and contract extension as new projects launch

What you’ll do

Requirements

A master's degree or higher in mathematics, logic, theoretical computer science, or a related field is required, along with strong rigorous proof-writing skills. Hands-on experience with Lean, Coq, Isabelle/HOL, Agda, or a comparable proof system is expected, with Lean 4 strongly preferred.