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
