Lean 4 Proof Engineer - Mathematical Formalization
STEM / Software, AI and Data
$170-$200/hr
About this role · Coding
About the Role What if your expertise in rigorous mathematics could directly shape how the world's most advanced AI systems reason, verify, and understand formal logic? 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 one of the most technically demanding and intellectually rewarding roles in AI training today. This is a fully remote, flexible contract role built for mathematicians who love working at the edge of what's formally possible. - 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