Lean Proof Engineer - Mathematical Formalization

What if your mathematical training could directly shape how AI reasons, proves, and understands the deepest structures of mathematics? We're looking for Lean 4 Proof Engineers to formalize advanced mathematical arguments for cutting-edge AI research — working at the frontier of what proof assistants can express, verify, and automate.

This is a fully remote, flexible contract role built for mathematicians who think in rigorous proof and feel at home inside a formal system. If you find genuine satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify — this role was made for you.

• Organization:
  Alignerr
• Type:
  Hourly Contract
• Location:
  
  Remote
• Commitment: 10–40 hours/week

• Translate informal mathematical proofs into precise, machine-verifiable Lean 4 formalizations, with an emphasis on clarity, structure, and correctness
• Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test the limits of existing proof assistants — especially where automated tools struggle or fail entirely
• Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond
• Reveal deeper patterns or generalizations implicit in the original mathematics through your formalizations

• Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Possess 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
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal, human‑written arguments into clean, structured, machine-verifiable proofs
• A mathematically mature problem‑solver who finds the frontier of formal verification genuinely exciting

• 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 fails or requires manual scaffolding
• Prior experience with data annotation, data quality evaluation, or AI training workflows
• Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies to research collaborators

• Work directly on cutting‑edge AI projects alongside world‑leading research labs
• Fully remote and flexible — structure your hours around your life, not the other way around
• Freelance autonomy: choose your own pace, work asynchronously, and collaborate globally
• Contribute to work that sits at the genuine intersection of mathematics and AI — helping machines understand human reasoning at its most rigorous
• Potential for ongoing work and contract extension as new projects launch