Mathematical Formalization Specialist
About this role
About the Role What if your deep mathematical expertise could directly shape how AI reasons, verifies, and understands proof — at the frontier of what machines can currently do? We're looking for mathematicians with hands-on experience in formal proof systems to translate rigorous human-written arguments into machine-verifiable Lean proofs. This is rare, high-impact work that sits at the intersection of pure mathematics and cutting-edge AI research — and it's work that automated tools simply cannot do alone. This is a fully remote, flexible contract role. If you're a mathematician who gets excited by precision, structural elegance, and the challenge of making a machine understand a beautiful proof, this is the role for you. - Organization: Alignerr - Type: Hourly Contract - Location: Remote - Commitment: Flexible — work on your own schedule What You'll Do - Translate informal mathematical proofs into Lean (Lean 3 or Lean 4) with an emphasis on clarity, structure, and correctness - Analyze domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures - Construct formalizations that probe and test the limits of existing proof assistants — especially where automation breaks down - Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines - Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms - Provide expert guidance on proof decomposition, lemma selection, and structuring strategies 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 (strongly preferred), Coq, Isabelle/HOL, Agda, or comparable formal proof systems - Passionate about formal verification, proof assistants, and the future of mechanized mathematics - Able to translate informal mathematical arguments into clean, well-structured formal proofs independently - Naturally precise, detail-oriented, and intellectually curious about the edge cases automated tools can't handle Nice to Have - Familiarity with type theory, the Curry–Howard correspondence, or proof automation techniques - Experience contributing to large-scale formalization projects such as mathlib - Exposure to theorem provers in contexts where manual scaffolding is required - Strong ability to articulate formalization decisions, edge cases, and reasoning strategies in writing Sample Work You Might Do - Formalize classical theorems and compare machine-verifiable structures against standard textbook arguments - Investigate where automated provers break down — and clearly articulate why (missing lemmas, insufficient libraries, complexity barriers, etc.) - Construct Lean proofs that surface deeper patterns or implicit generalizations within the original mathematics Why Join Us - Work on genuinely frontier problems — tasks where automated tools fail and human mathematical expertise is irreplaceable - Fully remote and flexible — structure your work around your schedule - Contribute directly to AI research that advances the reliability and reasoning capabilities of next-generation models - Freelance autonomy with the structure of meaningful, intellectually stimulating task-based work - Potential for ongoing work and contract extension as new research projects launch
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