Mathematical Formalization Specialist
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 to translate advanced mathematical arguments into machine-verifiable formalizations — working at the very edge of what proof assistants can do today. This is a fully remote, flexible contract role built for mathematicians who love precision, structural elegance, and the challenge of expressing rigorous human reasoning in a form a machine can understand. - 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 a focus on clarity, correctness, and structure - Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable sub-structures - Construct formalizations that test the limits of existing proof assistants, particularly where automated tools struggle or fail - Collaborate with AI researchers to design and refine formal verification strategies - Develop clean, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms - Guide proof decomposition, lemma selection, and structuring techniques for formal models - Investigate automated prover failure modes and articulate why they occur 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 proof assistants — Lean strongly preferred - Genuinely excited about formal verification, proof assistants, and the future of mechanized mathematics - Able to translate dense, informal mathematical arguments into precise, structured formal proofs - Self-directed and comfortable working independently on complex, open-ended problems Nice to Have - Familiarity with type theory, the Curry–Howard correspondence, or proof automation tools - Experience contributing to large-scale formalization projects (e.g., mathlib) - Exposure to theorem provers where automated reasoning frequently requires manual scaffolding - Strong communication skills for explaining formalization decisions, edge cases, and proof strategies Sample Work - Formalize classical proofs and compare machine-verifiable structures against textbook arguments - Investigate where automated provers break down and document why — missing lemmas, library gaps, complexity barriers - Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics Why Join Us - Work on genuinely cutting-edge AI 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 frontier of formal verification and AI mathematical reasoning - Potential for ongoing work and contract extension as new projects launch
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