Lean 4 Proof Engineer

Lean 4 Proof Engineer — Mathematical Formalization

About The Role
What if your deep mathematical expertise could directly shape how AI understands and reasons about formal proofs? We're looking for mathematicians and formal verification specialists to translate advanced mathematical arguments into machine-verifiable Lean 4 proofs — working at the absolute frontier of what proof assistants can do today. This is a fully remote, flexible contract role for mathematically mature problem-solvers who find genuine satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can understand and verify.
• Organization: Alignerr
• Type: Hourly Contract
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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, structure, and correctness
• Analyze generic and domain-specific proofs, identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test the limits of existing proof assistants — especially where tools struggle or fail entirely
• Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate where automated provers break down — and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.)
• 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 and mathematical reasoning 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 systems — Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into clean, structured formal proofs with minimal scaffolding
• A naturally precise thinker who appreciates structural elegance and the challenge of resolving gaps automated tools cannot yet bridge Nice to Have
• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
• Experience with large-scale formalization projects (e.g., 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 explaining formalization decisions, edge cases, and reasoning strategies Why Join Us
• Work directly with world-leading AI research teams and labs on cutting-edge projects
• Contribute to mapping the frontier of what formal verification can express, capture, and automate
• Gain rare, meaningful exposure to how advanced AI models are trained on formal mathematics
• Fully remote and asynchronous — work when and where it suits you
• Freelance autonomy with intellectually stimulating, high-impact work
• Potential for contract extension as new projects launch