Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About The Role

What if your mathematical expertise could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems to tackle problems that sit beyond the reach of automated tools — translating rigorous human arguments into machine-verifiable Lean proofs at the frontier of what formal verification can express.

This is a fully remote, flexible contract role designed for mathematicians who love precision, structural elegance, and the challenge of pushing proof assistants to their limits.

Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: Flexible hours, work on your own schedule

What You'll Do

Translate informal mathematical proofs into Lean (and related proof systems) with a focus on clarity, correctness, and structure Analyze domain-specific and general proofs to identify gaps, hidden assumptions, and formalizable sub-structures Construct formalizations that test and extend the limits of existing proof assistants — especially where automated tools struggle or fail 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 guidance on proof decomposition, lemma selection, and structuring techniques for formal models Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and more

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 a comparable formal proof system — Lean strongly preferred Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics Able to take a dense, informal mathematical argument and express it in a form a machine can verify Comfortable working independently and asynchronously in a remote environment

Nice to Have

Familiarity with type theory, the Curry–Howard correspondence, and proof automation tools Experience with large-scale formalization projects such as 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 to research collaborators

Why Join Us

Work on cutting-edge AI research projects alongside leading AI labs and research teams 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 AI reliability, formal reasoning, and high-integrity dataset creation Work at the true frontier of mathematics and computer science — on problems no automated tool can yet solve Potential for ongoing work and contract extension as new projects launch