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 boundary of what machines can understand and verify? We're looking for mathematicians and formal verification specialists to translate sophisticated human-written proofs into Lean 4, working at the cutting edge of mechanized mathematics and AI research. This is a fully remote, flexible contract role for researchers who love rigor, thrive on precision, and find genuine satisfaction in expressing elegant mathematical arguments in a form a machine can verify. - 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 proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures - Construct formalizations that test the limits of existing proof assistants, especially where automation struggles or fails - Investigate and articulate where automated provers break down — due to complexity, missing lemmas, insufficient libraries, or other factors - Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms - Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines - Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models - Formalize classical proofs and compare machine-verifiable structures against textbook arguments - Surface deeper patterns or generalizations implicit in the original mathematics 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 and mathematical reasoning — across algebra, analysis, topology, logic, or discrete mathematics - Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean strongly preferred - Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics - Able to translate informal arguments into clean, structured, machine-verifiable formal proofs - Mathematically mature and comfortable working at the frontier of what proof assistants can currently express 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, data quality, or evaluation systems - Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies Why Join Us - Work on cutting-edge AI projects alongside leading research labs - Fully remote and flexible — work when and where it suits you - Freelance autonomy with the structure of meaningful, intellectually stimulating work - Contribute directly to advancing the capabilities of AI in formal reasoning and mathematics - Potential for ongoing work and contract extension as new projects launch
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