Researcher - Lean 4 & Formal Proof Systems
About this role
About the Role What if your deep mathematical training could directly shape how AI understands and reasons about formal proofs — advancing the frontier of mechanized mathematics for millions of future users? We're looking for mathematicians and formal verification specialists to write and formalize advanced mathematical proofs in Lean 4 for cutting-edge AI research. This role sits at the intersection of mathematics and computer science, translating rigorous human arguments into precise, machine-verifiable formalizations that push the limits of what proof assistants can express and automate. This is a fully remote, flexible contract role designed for researchers who love structure, precision, and working at the edge of what's formally possible. - 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 generic and domain-specific proofs, identifying 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 highly 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 - Formalize classical proofs and compare machine-verifiable structures against textbook arguments - Investigate and articulate where automated provers break down — due to complexity, missing lemmas, insufficient libraries, or other factors - 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 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, structured formal proofs with precision and care - A mathematically mature problem-solver who finds satisfaction in expressing dense, elegant human arguments in a form a machine can verify 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 and teams - 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 the capabilities of AI at the frontier of formal mathematics - Potential for ongoing work and contract extension as new projects launch - Collaborate with a global community of researchers tackling some of the hardest problems in formal verification
Application listings
Choose a source listing and check its country requirements.