Lean 4 Proof Engineer - Mathematical Formalization
STEM / Software, AI and Data
$170-$200/hr
About this role · Coding
About the Role What if your deep mathematical expertise could directly shape how AI reasons, proves, and understands the foundations of mathematics? We're looking for Lean 4 Proof Engineers to translate rigorous human-written 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 for mathematicians who love precision, structural elegance, and the challenge of making formal verification go further than it's ever gone before. - 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 correctness - Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures - Push the limits of existing proof assistants by constructing formalizations where tools struggle or fail - Collaborate with AI researchers to design, refine, and evaluate formal verification strategies - Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms - Provide expert guidance on proof decomposition, lemma selection, and structuring techniques - Formalize classical proofs and compare machine-verifiable structures against textbook arguments - Articulate and document where and why automated provers break down — complexity, missing lemmas, insufficient libraries, and more - Surface deeper patterns or generalizations implicit in the original mathematics through your Lean formalizations Who You Are - Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field - Possess 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), Coq, Isabelle/HOL, Agda, or comparable systems — Lean strongly preferred - Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics - Able to translate informal arguments into clean, well-structured formal proofs - A mathematically mature problem-solver who finds satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify Nice to Have - Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools - Experience with 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, data quality, or AI evaluation systems - Strong written communication skills for documenting formalization decisions, edge cases, and reasoning strategies Why Join Us - Work on frontier AI projects alongside leading research labs and teams - Fully remote and flexible — structure your work around your schedule - Freelance autonomy with intellectually stimulating, high-impact work - Gain rare exposure to how advanced AI models are trained on formal mathematical reasoning - Contribute to expanding the boundary of what machines can formally understand and verify - Potential for ongoing work and contract extension as new projects launch