Lean 4 Proof Engineer - Mathematical Formalization

About The Role

We're looking for Lean 4 Proof Engineers to translate sophisticated human-written mathematical arguments into precise, machine-verifiable formalizations — working at the frontier of what modern proof assistants can express and automate. This is a fully remote, flexible contract role built for mathematicians who love working at the edge of what's formally possible.

Organization & Commitment

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: 10–40 hours/week

What You'll Do

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, structure, and machine-verifiable correctness
• Analyze generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and expand the limits of existing proof assistants, especially where tools struggle or fail
• Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, or structural issues
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

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
• Have hands-on experience with Lean (Lean 3 or Lean 4 strongly preferred), Coq, Isabelle/HOL, Agda, or comparable formal systems
• Are deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Can translate dense, informal mathematical arguments into clean, structured formal proofs
• Thrive at the intersection of mathematics and computer science, where precision and structural elegance matter

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 manual scaffolding
• Prior experience with data annotation, quality evaluation, or AI training workflows
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work on cutting-edge AI projects alongside leading research labs and frontier AI teams
• Fully remote and flexible — work when and where suits you, on your own schedule
• Freelance autonomy with meaningful, intellectually stimulating work
• Contribute to research that is actively shaping the future of formal reasoning in AI
• Potential for ongoing work and contract extension as new projects launch