Lean 4 Proof Engineer - Mathematical Formalization
About this role
About the Role What if your deep mathematical expertise could directly shape how AI understands and reasons about formal proof? We're looking for Lean 4 Proof Engineers to translate advanced mathematical arguments into machine-verifiable formalizations — working at the absolute frontier of what proof assistants can express, capture, and automate. This is a fully remote, flexible contract role for mathematicians who thrive on precision, structural elegance, and the challenge of making rigorous human reasoning legible to a machine. - 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, correctness, and structure - Analyze proofs across domains — algebra, analysis, topology, logic, discrete math — identifying gaps, hidden assumptions, and formalizable substructures - Construct formalizations that test and extend the limits of existing proof assistants, especially where automation breaks down - Investigate why automated provers fail — complexity barriers, missing lemmas, insufficient libraries — and articulate those failure modes clearly - Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms - Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines - Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics - Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models 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 and mathematical reasoning across one or more of: algebra, analysis, topology, logic, or discrete mathematics - Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable formal proof system — Lean 4 strongly preferred - Genuinely excited about formal verification, proof assistants, and the future of mechanized mathematics - Able to translate dense, informal mathematical arguments into clean, structured, machine-checkable proofs - Self-directed and comfortable working independently in an asynchronous remote environment 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, data quality, or evaluation systems - Strong communication skills for documenting formalization decisions, edge cases, and reasoning strategies The Ideal Candidate You're a mathematically mature problem-solver who finds genuine satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify. You appreciate precision, structural beauty, and the intellectual challenge of resolving gaps that automated tools cannot yet bridge. You're energized by working at the frontier — not frustrated by it. Why Join Us - Work on cutting-edge AI projects alongside world-leading research labs - Fully remote and flexible — work when and where it suits you - Freelance autonomy with the structure of meaningful, intellectually rigorous work - Direct exposure to how advanced AI models are trained and evaluated - Contribute to work that maps the outer limits of what formal verification can achieve - Potential for ongoing work and contract extension as new projects launch
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