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 understands and reasons about formal proof? We're looking for Lean 4 Proof Engineers to translate advanced mathematical arguments into machine-verifiable formalizations — working at the absolute frontier of what proof assistants can express, capture, and automate.

This is a fully remote, flexible contract role for mathematicians who thrive on precision, structural elegance, and the challenge of making rigorous human reasoning legible to a machine.

• 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, correctness, and structure
• Analyze proofs across domains — algebra, analysis, topology, logic, discrete math — identifying gaps, hidden assumptions, and formalizable substructures
• Construct formalizations that test and extend the limits of existing proof assistants, especially where automation breaks down
• Investigate why automated provers fail — complexity barriers, missing lemmas, insufficient libraries — and articulate those failure modes clearly
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
  
  

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 and mathematical reasoning across one or more of: 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 4 strongly preferred
• Genuinely excited about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal mathematical arguments into clean, structured, machine-checkable proofs
• Self-directed and comfortable working independently in an asynchronous remote environment
  
  

Nice to Have

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

The Ideal Candidate

You're a mathematically mature problem-solver who finds genuine satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify. You appreciate precision, structural beauty, and the intellectual challenge of resolving gaps that automated tools cannot yet bridge. You're energized by working at the frontier — not frustrated by it.

Why Join Us

• Work on cutting-edge AI projects alongside world-leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually rigorous work
• Direct exposure to how advanced AI models are trained and evaluated
• Contribute to work that maps the outer limits of what formal verification can achieve
• Potential for ongoing work and contract extension as new projects launch

---