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 — especially Lean — to help push the boundaries of what machine-verifiable mathematics can express. This is a fully remote, flexible contract role working alongside leading AI research labs. You'll tackle proofs that automated tools can't yet handle, helping map the true frontier of formal verification. - Organization: Alignerr - Type: Hourly Contract - Location: Remote - Commitment: Flexible What You'll Do - Translate informal mathematical proofs into Lean (and related proof systems) with a focus on clarity, structure, and machine-verifiable correctness - Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable sub-structures - Build formalizations that probe the limits of current proof assistants, especially where automation breaks down - 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 - Advise on proof decomposition, lemma selection, and structuring techniques for formal models Who You Are - 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 a comparable system — Lean strongly preferred - Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics - Ability to translate dense, informal arguments into clean, structured formal proofs - Comfortable working independently on technically demanding, open-ended problems Nice to Have - Familiarity with type theory, the Curry–Howard correspondence, and proof automation tooling - Experience contributing to large-scale formalization projects (e.g., mathlib) - Exposure to theorem provers in contexts where automated reasoning frequently fails or requires manual scaffolding - Strong communication skills for documenting formalization decisions, edge cases, and reasoning strategies 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, library gaps, etc.) - Construct Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics Why Join Us - Work on some of the most intellectually demanding problems at the intersection of mathematics and AI - Fully remote and flexible — work when and where it suits you - Freelance autonomy with meaningful, well-defined 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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