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: AlignerrType: Hourly ContractLocation: RemoteCommitment: 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 correctnessAnalyze domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structuresConstruct formalizations that test the limits of existing proof assistants — especially where automated tools struggle or failCollaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelinesDevelop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idiomsProvide guidance on proof decomposition, lemma selection, and structuring techniques for formal modelsInvestigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and moreCreate 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 fieldHave a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathHave hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean strongly preferredAre deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematicsCan 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 toolsExperience contributing to large-scale formalization projects such as MathlibExposure to theorem provers where automated reasoning frequently fails or requires manual scaffoldingPrior experience with data annotation, data quality, or AI evaluation systemsStrong 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 labsFully remote and flexible — work when and where it suits youFreelance autonomy with the structure of meaningful, intellectually stimulating workOperate directly at the frontier of formal verification and AI — helping map what machines can and cannot yet provePotential for ongoing work and contract extension as new projects launch