Applied Formal Methods Researcher (Lean 4)
About this role
About the Role What if your deep mathematical training could directly shape how AI reasons, proves, and understands mathematics at a fundamental level? We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — working at the precise intersection of rigorous mathematics and cutting-edge AI research. This is a fully remote, flexible contract role designed for mathematicians who are passionate about formal verification and want their expertise to matter at scale. - Organization: Alignerr - Type: Hourly Contract - Location: Remote - Commitment: 10–40 hours/week What You'll Do - Translate informal mathematical proofs into clean, machine-verifiable Lean 4 formalizations with an emphasis on clarity, structure, and correctness - Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures - Construct formalizations that probe the limits of existing proof assistants, especially where automation fails or falls short - Collaborate with researchers 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 expert 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 beyond - 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 math - Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof systems — Lean strongly preferred - Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics - Able to translate informal mathematical arguments into precise, clean, structured formal proofs - Thrive working independently and asynchronously at the frontier of a fast-moving field 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 evaluation, or AI training workflows - Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies Why Join Us - Work directly with world-leading AI research teams on projects at the cutting edge of formal mathematics and AI - Fully remote and flexible — work when and where it suits you - Freelance autonomy with meaningful, intellectually stimulating work - Gain rare exposure to how advanced AI models are trained to reason mathematically - Contribute to defining the frontier of what formal verification can express, capture, and automate - Potential for ongoing work and contract extension as new projects launch
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