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 solid 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

📌 Lean 4 Proof Engineer - Mathematical Formalization (Montreal)
🏢 Alignerr
📍 Montreal