Mathematical Formalization Specialist (Lean / Formal Proof Systems)
About this role
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: Alignerr - Type: Hourly Contract - Location: Remote - Commitment: Flexible, task-based What You'll Do - Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness - Analyze proofs across mathematical domains — 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 AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines - Develop clean, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms - Provide 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 arguments - Investigate 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 Who You Are Required: - Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field - Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics - Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal proof systems — Lean strongly preferred - Genuine enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics - Ability 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 tools - Experience contributing to large-scale formalization projects such as mathlib - Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding - Strong 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 labs - Fully remote and flexible — work when and where it suits you - Freelance autonomy with the structure of meaningful, intellectually stimulating work - Contribute directly to advancing the reliability and reasoning capabilities of next-generation AI - Potential for ongoing work and contract extension as new projects launch
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