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 the future of AI reasoning? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs — working at the precise boundary where human mathematical intuition meets the rigorous demands of proof assistants. This is a fully remote, flexible contract role for researchers who love structure, precision, and pushing the limits of what formal systems can express. If you find satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify, this role was built 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 proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures Construct formalizations that test the limits of existing proof assistants, especially where automation breaks down 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 fail — and clearly articulate why (complexity, missing lemmas, library gaps, etc.) Create Lean proofs that 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 systems — Lean strongly preferred Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics Able to translate informal arguments into clean, well-structured formal proofs with precision and care 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, data quality, or AI evaluation workflows 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 research labs Fully remote and flexible — work when and where it suits you Freelance autonomy with the structure of meaningful, high-impact technical work Contribute directly to advancing what AI can understand, reason about, and verify in mathematics Potential for ongoing work and contract extension as new projects launch