Lean 4 Proof Engineer - Mathematical Formalization

Lean 4 Proof Engineer — Mathematical Formalization

About the Role

What if your deep mathematical training could directly shape the future of AI — and help machines understand the most rigorous arguments the human mind can produce?

We're looking for expert mathematicians with hands-on experience in formal proof systems to translate advanced mathematical reasoning into machine-verifiable Lean 4 code. This role sits at the frontier of what proof assistants can express, capture, and automate — and you'll be the one mapping that frontier.

This is a fully remote, flexible contract role for mathematicians who care deeply about precision, structure, and the art of formal argumentation.

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

What You'll Do

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on correctness and clarity
• Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures
• Construct formalizations that test and expose the limits of existing proof assistants
• Collaborate with AI researchers to design and evaluate strategies for improving formal verification pipelines
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Guide proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers break down — and articulate precisely why
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

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 4 strongly preferred
• Thrive at the intersection of mathematics and formal computer science
• Take satisfaction in translating dense, elegant human arguments into forms a machine can fully verify
• Appreciate precision, structural beauty, and the challenge of resolving gaps that automated tools cannot yet bridge

Nice to Have

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
• Experience contributing to large-scale formalization projects (e.g., Mathlib)
• Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
• Prior experience with data annotation, quality evaluation, or AI training workflows
• Strong communication skills for articulating formalization decisions, edge cases, and proof strategies

Why Join Us

• Work directly on cutting-edge AI research alongside leading labs and researchers
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually rigorous work
• Operate at the frontier of mechanized mathematics — pushing what formal verification can achieve
• Potential for ongoing work and contract extension as new projects launch