Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About The Role What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems — especially Lean — to tackle problems that sit beyond the reach of automated tools. This is a fully remote, flexible contract role at the intersection of mathematics and computer science. You'll work on genuinely hard problems, translating rigorous human arguments into machine-verifiable formalizations that help map the frontier of what proof assistants can express, capture, and automate. Organization: AlignerrType: Hourly ContractLocation: RemoteCommitment: Flexible, task-based What You'll Do Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctnessAnalyze proofs across mathematical domains — 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 clean, reproducible proof scripts aligned with mathematical best practices and proof assistant idiomsProvide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models Sample Work You Might Do Formalize 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.)Write Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics Required Who You Are Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related fieldStrong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematicsHands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal proof systems — Lean strongly preferredGenuine enthusiasm for formal verification, proof assistants, and the future of mechanized mathematicsAbility to translate dense, informal mathematical arguments into clean, structured formal proofs 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 scaffoldingStrong communication skills for articulating formalization decisions, edge cases, and reasoning strategies The Ideal Candidate You're a mathematically mature problem-solver who finds genuine satisfaction in taking a dense, elegant argument and expressing it in a form a machine can understand. You appreciate precision, structural beauty, and the intellectual challenge of resolving gaps that automated tools cannot yet bridge. You don't just do mathematics — you think carefully about how mathematics is done. Why Join Us Work on cutting-edge AI research projects alongside leading research labsFully remote and flexible — work when and where it suits youFreelance autonomy with the structure of meaningful, intellectually stimulating workContribute directly to advancing the reliability and reasoning capabilities of next-generation AIPotential for ongoing work and contract extension as new projects launch