Researcher - Lean 4 & Formal Proof Systems

Researcher — Lean 4 & Formal Proof Systems (AI Training) About The Role What if your deep mathematical training could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians and formal verification specialists to translate sophisticated human-written proofs into machine-verifiable Lean 4 formalizations — pushing the boundary of what proof assistants can express, capture, and automate. This is a fully remote, flexible contract role built for researchers who love rigor, structural precision, and working at the frontier of mathematics and computer science. Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: 10–40 hours/week What You'll Do Translate informal mathematical proofs into clean, well-structured Lean 4 formalizations with an emphasis on clarity and correctness Analyze domain-specific and general 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 Investigate breakdown points in automated provers and articulate precisely why they occur (complexity, missing lemmas, library gaps, etc.) Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms Collaborate with researchers to design and refine strategies for improving formal verification pipelines Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models Formalize classical proofs and surface 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 mathematics Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof assistants — Lean 4 strongly preferred Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics Able to take a dense, elegant human argument and express it in a form a machine can verify 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 written communication skills for explaining formalization decisions, edge cases, and reasoning strategies Why Join Us Work directly on cutting-edge AI research projects alongside 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 to advancing the frontier of what formal verification and AI can achieve together Potential for ongoing work and contract extension as new projects launch