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 push the boundaries of what machines can reason about?

We're looking for mathematicians with formal verification expertise to translate rigorous human-written proofs into machine-verifiable Lean 4 formalizations. This role sits at the frontier of mathematics and computer science, working on problems that often lie beyond the reach of automated provers. You'll help map — and expand — what formal verification can express, capture, and automate.

This is a fully remote, flexible contract role designed for mathematically mature problem-solvers who find beauty in precision and satisfaction in resolving what automated tools cannot yet bridge.

• 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 clarity, structure, and correctness
• Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test the limits of existing proof assistants — especially where current tools struggle or fail
• 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 proof assistant idioms
• Provide 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, insufficient libraries, and beyond
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Uncover 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 formal systems — Lean 4 strongly preferred
• Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into clean, structured, machine-verifiable proofs

Nice to Have

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

Why Join Us

• Work on genuinely frontier problems at the intersection of mathematics and AI
• Collaborate with leading AI research teams pushing the state of the art in formal reasoning
• Fully remote and flexible — structure your work around your life
• Freelance autonomy with access to some of the most intellectually demanding problems in the field
• Exposure to advanced LLMs and how formal mathematics is used to train and evaluate them
• Potential for contract extension as new projects launch