Lean 4 Proof Engineer - Mathematical Formalization
About this role
About the Role What if your deep mathematical training could directly shape the future of AI — and help machines understand the most rigorous arguments the human mind can produce? We're looking for expert mathematicians with hands-on experience in formal proof systems to translate advanced mathematical reasoning into machine-verifiable Lean 4 code. This role sits at the frontier of what proof assistants can express, capture, and automate — and you'll be the one mapping that frontier. This is a fully remote, flexible contract role for mathematicians who care deeply about precision, structure, and the art of formal argumentation. - 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 correctness and clarity - Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures - Construct formalizations that test and expose the limits of existing proof assistants - Collaborate with AI researchers to design and evaluate strategies for improving formal verification pipelines - Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms - Guide proof decomposition, lemma selection, and structuring techniques for formal models - Investigate where automated provers break down — and articulate precisely why - 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 - 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 4 strongly preferred - Thrive at the intersection of mathematics and formal computer science - Take satisfaction in translating dense, elegant human arguments into forms a machine can fully verify - Appreciate precision, structural beauty, and the challenge of resolving gaps that automated tools cannot yet bridge Nice to Have - Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools - Experience contributing to large-scale formalization projects (e.g., 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 articulating formalization decisions, edge cases, and proof strategies Why Join Us - Work directly on cutting-edge AI research alongside leading labs and researchers - Fully remote and flexible — work when and where it suits you - Freelance autonomy with the structure of meaningful, intellectually rigorous work - Operate at the frontier of mechanized mathematics — pushing what formal verification can achieve - Potential for ongoing work and contract extension as new projects launch
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