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 setting 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

📌 Mathematical Formalization Specialist (Toronto)
🏢 Alignerr
📍 Toronto