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 rigorous human arguments into machine-verifiable formalizations — working at the bleeding edge of what proof assistants can express, capture, and automate. This is a fully remote, flexible contract role built for mathematicians who are passionate about precision, formal verification, and the challenge of pushing modern proof assistants to their limits. - Organization: Alignerr - Type: Hourly Contract - Location: Remote - Commitment: Flexible 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 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 - Advise on proof decomposition, lemma selection, and structuring techniques for formal models 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 formal systems — Lean strongly preferred - Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics - Able to translate dense informal arguments into clean, well-structured formal proofs - Self-directed and reliable when working independently on technically demanding tasks 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 breaks down or requires manual scaffolding - Strong communication skills for articulating formalization decisions, edge cases, and proof strategies Sample Work You Might Do - Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments - Investigate where automated provers break down — and document exactly why (complexity, missing lemmas, library gaps, etc.) - Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics - Help map the frontier of what current formal verification tools can and cannot yet handle 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 rigorous work - Contribute to a growing field where your expertise directly advances the reliability and reasoning capability of AI systems - Potential for ongoing work and contract extension as new formalization projects launch
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