Lean 4 Proof Engineer - Mathematical Formalization

Lean 4 Proof Engineer — Mathematical Formalization (AI Training)About The RoleWhat if your deep mathematical expertise could directly shape the future of AI reasoning? We're looking for Lean 4 Proof Engineers to formalize advanced mathematical arguments into machine-verifiable proofs — working at the very frontier of what modern proof assistants can express, capture, and automate.This is a fully remote, flexible contract role built for mathematicians who live at the intersection of rigorous proof construction and formal verification. If you find genuine satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can understand, this role was designed for you.Organization: AlignerrType: Hourly ContractLocation: RemoteCommitment: 10–40 hours/weekWhat You'll DoTranslate informal mathematical proofs into Lean 4 (and related proof systems) with emphasis on clarity, structure, and correctnessAnalyze generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structuresConstruct formalizations that test the limits of existing proof assistants, especially where automated tools struggle or failCollaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelinesDevelop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idiomsProvide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal modelsFormalize classical proofs and compare machine-verifiable structures against textbook argumentsInvestigate where automated provers break down — and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.)Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematicsWho You AreHold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related fieldPossess a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematicsHave hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — with Lean strongly preferredDeeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematicsAble to translate informal mathematical arguments into clean, structured, and machine-checkable formalizationsComfortable working independently with precision and intellectual rigorNice to HaveFamiliarity 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 strategiesWhy Join UsWork on cutting-edge AI projects alongside world-leading research labsFully remote and flexible — work when and where it suits youFreelance autonomy with the structure of meaningful, intellectually stimulating workGet direct exposure to how advanced AI models are trained and evaluated on mathematical reasoningContribute to mapping the frontier of what formal verification can achievePotential for ongoing work and contract extension as new projects launch