Researcher - Lean 4 & Formal Proof Systems
About this role
About the Role What if your deep mathematical expertise could directly shape how AI reasons about formal proofs — pushing the frontier of what machines can understand and verify? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs for cutting-edge AI research. This role sits at the intersection of mathematics and computer science, working on problems that lie beyond the reach of current automated provers. This is a fully remote, flexible contract role built for researchers who love rigor, precision, and the challenge of expressing elegant human reasoning in a form a machine can trust. - 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 and general mathematical arguments — identifying gaps, hidden assumptions, and formalizable sub-structures - Construct formalizations that test and extend the limits of existing proof assistants, especially where automation breaks down - Investigate failure modes in automated provers and articulate precisely why they occur — complexity barriers, missing lemmas, insufficient libraries - Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms - Collaborate with researchers to design and refine strategies for improving formal verification pipelines - Create Lean proofs that reveal deeper patterns or generalizations implicit in original mathematical arguments - Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models Who You Are - Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field - Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics - Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal proof systems — Lean 4 strongly preferred - Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics - Ability to take dense, informal arguments and express them in clean, structured, machine-verifiable form - Self-directed and comfortable working at the frontier, where the right path isn't always obvious 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, evaluation systems, or AI training workflows - Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies Why Join Us - Work on cutting-edge AI research projects in collaboration with leading AI labs - Fully remote and flexible — work when and where it suits you - Freelance autonomy with the structure of meaningful, intellectually demanding work - Contribute directly to expanding what AI can understand and verify in advanced mathematics - Potential for ongoing work and contract extension as new projects launch
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