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 recent projects launch

📌 Lean 4 Proof Engineer (Montreal)
🏢 Alignerr
📍 Montreal