Researcher - Lean 4 & Formal Proof Systems

Researcher — Lean 4 & Formal Proof Systems (AI Training) About The Role What if your expertise in rigorous mathematical proof could directly shape the future of AI reasoning? We're looking for mathematicians and formal verification specialists to translate sophisticated human-written proofs into machine-verifiable Lean 4 formalizations — working at the very frontier of what proof assistants can express, capture, and automate. This is a fully remote, flexible contract role for researchers who love precision, structural elegance, and the challenge of bridging human mathematical intuition with formal systems. Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: 10–40 hours/week What You'll Do Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures Construct formalizations that test and extend the limits of existing proof assistants Investigate where automated provers break down and articulate why — whether due to complexity, missing lemmas, or library gaps Collaborate with researchers to design, refine, and evaluate formal verification strategies Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms Guide proof decomposition, lemma selection, and structural decisions for complex formal models Create Lean proofs that reveal deeper patterns or generalizations implicit in classical mathematical arguments 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 mathematics Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable system — Lean 4 strongly preferred Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics Able to translate dense, informal mathematical arguments into precise, structured formal proofs with clarity and confidence 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 significant manual scaffolding Prior experience with data annotation, evaluation systems, or AI training workflows Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies Why Join Us Work on cutting-edge AI projects alongside leading research labs and teams Fully remote and flexible — work when and where it suits you Freelance autonomy with the structure of meaningful, intellectually demanding work Contribute directly to advancing what AI can understand and reason about in formal mathematics Potential for ongoing work and contract extension as new projects launch