Researcher - Lean 4 & Formal Proof Systems
About this role
About the Role What if your deep mathematical training could directly shape how AI reasons about formal proofs — pushing the boundary of what machines can understand and verify? We're looking for mathematicians and formal verification experts to translate sophisticated mathematical arguments into precise, machine-verifiable Lean proofs for cutting-edge AI research. This is a fully remote, flexible contract role. If you find satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can understand — this is the role for you. - 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 domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures - Construct formalizations that test the limits of existing proof assistants — especially where automated 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 why — complexity, missing lemmas, insufficient libraries, and more - 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 math - Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean strongly preferred - Are deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics - Can translate informal mathematical arguments into clean, structured formal proofs with precision 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, data quality, or AI evaluation systems - Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies Why Join Us - Work on cutting-edge AI research projects alongside world-leading AI labs - Fully remote and flexible — work when and where it suits you - Freelance autonomy with the structure of meaningful, intellectually stimulating work - Operate directly at the frontier of formal verification and AI — helping map what machines can and cannot yet prove - Potential for ongoing work and contract extension as new projects launch
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