Lean 4 Proof Engineer - Mathematical Formalization

Lean 4 Proof Engineer — Mathematical Formalization (AI Training)

About The Role

What if your deep mathematical expertise could directly shape how AI reasons, proves, and understands the foundations of mathematics? We're looking for Lean 4 Proof Engineers to translate rigorous human-written arguments into machine-verifiable formalizations — working at the very frontier of what proof assistants can express and automate.

This is a fully remote, flexible contract role for mathematicians who love precision, structural elegance, and the challenge of making formal verification go further than it's ever gone before.

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

What You'll Do

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, structure, and correctness
• Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
• Push the limits of existing proof assistants by constructing formalizations where tools struggle or fail
• Collaborate with AI researchers to design, refine, and evaluate formal verification strategies
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Articulate and document where and why automated provers break down — complexity, missing lemmas, insufficient libraries, and more
• Surface deeper patterns or generalizations implicit in the original mathematics through your Lean formalizations

Who You Are

• 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 systems — Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into clean, well-structured formal proofs
• A mathematically mature problem-solver who finds satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify

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
• Prior experience with data annotation, data quality, or AI evaluation systems
• Strong written communication skills for documenting formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work on frontier AI projects alongside leading research labs and teams
• Fully remote and flexible — structure your work around your schedule
• Freelance autonomy with intellectually stimulating, high-impact work
• Gain rare exposure to how advanced AI models are trained on formal mathematical reasoning
• Contribute to expanding the boundary of what machines can formally understand and verify
• Potential for ongoing work and contract extension as new projects launch