Lean 4 Proof Engineer — Mathematical Formalization

About The Role

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 Strong 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