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 reasons about formal proofs — pushing the boundary of what machines can understand and verify? We're looking for mathematicians and formal verification experts to translate sophisticated mathematical arguments into precise, machine-verifiable Lean proofs for cutting-edge AI research. This is a fully remote, flexible contract role. If you find satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can understand — this is the role for you. 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 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 Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines Develop 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 Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and more 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 Have 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 formal systems — Lean strongly preferred Are deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics Can translate informal mathematical arguments into clean, structured formal proofs with precision
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 AI evaluation systems Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
Work on cutting-edge AI research projects alongside world-leading AI labs Fully remote and flexible — work when and where it suits you Freelance autonomy with the structure of meaningful, intellectually stimulating work Operate directly at the frontier of formal verification and AI — helping map what machines can and cannot yet prove Potential for ongoing work and contract extension as new projects launch