Researcher - Lean 4 & Formal Proof Systems
About this role
About the Role What if your mathematical expertise 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 specialists to translate sophisticated mathematical arguments into machine-verifiable Lean proofs, working on problems that sit at the very frontier of what automated systems can handle today. This is a fully remote, flexible contract role designed for researchers who love rigor, structure, and the intellectual challenge of making the implicit explicit. - Organization: Alignerr - Type: Hourly Contract - Location: Remote - Commitment: 10–40 hours/week What You'll Do - Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 (and related proof systems) - Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures - Construct formalizations that test and extend the limits of existing proof assistants, especially where automation struggles or fails - Investigate the breakdown points of automated provers and articulate the underlying reasons — complexity, missing lemmas, library gaps, and more - Collaborate with research teams to design, refine, and evaluate strategies for improving formal verification pipelines - Develop highly 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 - Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics Who You Are - Holds a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field - Deeply grounded in rigorous proof construction across areas such as algebra, analysis, topology, logic, or discrete mathematics - Experienced with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean strongly preferred - Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics - Able to translate dense, informal mathematical arguments into clean, structured, formally verified proofs - Finds satisfaction in resolving the 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 such as Mathlib - Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding - Prior experience with data annotation, data quality, or evaluation systems - Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies Why Join Us - Work directly on cutting-edge AI research projects alongside leading research labs - Fully remote and flexible — work when and where it suits you - Freelance autonomy with meaningful, intellectually stimulating work at the frontier of formal mathematics - Gain rare exposure to how advanced AI models are trained on formal reasoning tasks - Potential for ongoing work and contract extension as new projects launch
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