Lean 4 Proof Engineer - Mathematical Formalization

Lean 4 Proof Engineer — Mathematical Formalization

About The Role

What if your deepest mathematical instincts could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians with serious proof-writing chops to formalize advanced mathematical arguments in Lean 4 — working at the very frontier of what modern proof assistants can express, verify, and automate.

This is a fully remote, flexible contract role built for mathematicians who love precision, structure, and the challenge of translating elegant human reasoning into machine-verifiable form.

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

What You'll Do

• Translate informal mathematical proofs into rigorous, machine-verifiable Lean 4 formalizations with an emphasis on clarity, correctness, and structure
• Identify gaps, hidden assumptions, and formalizable sub-structures within generic and domain-specific proofs
• Construct formalizations that probe the limits of existing proof assistants — especially where automated 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 and articulate the breakdown points of automated provers — complexity barriers, missing lemmas, insufficient libraries, and more
• Surface deeper patterns or generalizations implicit in the original mathematics through Lean proof construction

Who You Are

• Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Possess 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 is 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 formal proofs with precision and care

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, evaluation systems, or AI training workflows
• Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies to non-specialist collaborators

Why Join Us

• Work on cutting-edge AI projects alongside leading research labs and AI teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Get direct exposure to advanced LLMs and how they are trained on formal mathematical reasoning
• Contribute to work that is actively pushing the boundary of what AI can understand and verify
• Potential for ongoing work and contract extension as new projects launch