Lean 4 Proof Engineer - Mathematical Formalization

What if your mathematical expertise could directly shape how AI understands and reasons about formal proof? We're looking for skilled mathematicians to translate rigorous human arguments into machine-verifiable Lean 4 formalizations — working at the very frontier of what proof assistants can express, capture, and automate.

This is a fully remote, flexible contract role built for mathematicians who care deeply about formal verification and want their work to matter at the cutting edge of AI research.

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

What You'll Do

- 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 push the limits of existing proof assistants - especially where automation fails or falls short
- Collaborate with 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 precisely why - complexity, missing lemmas, library gaps, and beyond




- 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
- Have 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 proof systems - Lean strongly preferred
- Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Able to take a dense, elegant human argument and express it in a form a machine can verify - cleanly and completely

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 significant manual scaffolding
- Prior experience with data annotation, data quality, or evaluation systems
- Solid communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

- Work on genuinely frontier AI research alongside leading labs and research teams
- Fully remote and flexible - work when and where it suits you
- Freelance autonomy with the structure of intellectually stimulating, high-impact work
- Contribute directly to expanding what formal verification can express and automate
- Potential for ongoing work and contract extension as new projects launch

📌 Lean 4 Proof Engineer (Toronto)
🏢 Alignerr
📍 Toronto