Mathematical Formalization Specialist (Lean / Formal Proof Systems)
About this role
About the Role What if your deep mathematical training could directly shape how AI reasons, verifies, and understands formal logic? We're looking for mathematicians with hands-on experience in formal proof systems — particularly Lean — to work at the intersection of rigorous mathematics and cutting-edge AI research. This is a fully remote, flexible contract role built for mathematically mature problem-solvers who find satisfaction in translating elegant human arguments into precise, machine-verifiable form. You'll work on proofs that push the boundaries of what automated tools can currently handle — helping map the frontier of formal verification itself. - 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 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 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 - Investigate where automated provers break down and articulate why — uncovering complexity, missing lemmas, or insufficient libraries 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 - Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics - Able to translate informal arguments into clean, well-structured formal proofs - Mathematically mature — you notice the gaps that others skip over and know how to resolve them Nice to Have - Familiarity with type theory, the Curry–Howard correspondence, and proof automation tools - Experience with large-scale formalization projects (e.g., mathlib) - Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding - Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies Sample Work You Might Do - Formalize classical proofs and compare machine-verifiable structures against textbook arguments - Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics - Identify precisely where and why automated provers fail on a given class of problems Why Join Us - Work on some of the most technically demanding AI research problems in existence today - Fully remote and flexible — work when and where it suits you - Freelance autonomy with the structure of meaningful, high-impact, task-based work - Contribute directly to advancing the reliability and reasoning capability of frontier AI systems - Potential for ongoing work and contract extension as new projects launch
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