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 push the boundaries of what machines can reason about? We're looking for mathematicians with formal verification expertise to translate rigorous human-written proofs into machine-verifiable Lean 4 formalizations. This role sits at the frontier of mathematics and computer science, working on problems that often lie beyond the reach of automated provers. You'll help map — and expand — what formal verification can express, capture, and automate. This is a fully remote, flexible contract role designed for mathematically mature problem-solvers who find beauty in precision and satisfaction in resolving what automated tools cannot yet bridge. - 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 clarity, structure, and correctness - Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures - Construct formalizations that test the limits of existing proof assistants — especially where current tools struggle or fail - Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines - Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms - Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models - Investigate where automated provers break down and articulate precisely why — complexity, missing lemmas, insufficient libraries, and beyond - Formalize classical proofs and compare machine-verifiable structures against textbook arguments - Uncover 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), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean 4 strongly preferred - Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics - Able to translate informal arguments into clean, structured, machine-verifiable proofs 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, evaluation systems, or AI training workflows - Strong communication skills for explaining formalization decisions, edge cases, and proof strategies Why Join Us - Work on genuinely frontier problems at the intersection of mathematics and AI - Collaborate with leading AI research teams pushing the state of the art in formal reasoning - Fully remote and flexible — structure your work around your life - Freelance autonomy with access to some of the most intellectually demanding problems in the field - Exposure to advanced LLMs and how formal mathematics is used to train and evaluate them - Potential for contract extension as new projects launch
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