Lean 4 Proof Engineer - Mathematical Formalization

About The Role

What if your deep mathematical training could directly influence how AI systems reason, verify, and understand formal logic? We're looking for Lean 4 Proof Engineers to translate advanced mathematical arguments into machine-verifiable formalizations --- working at the cutting edge of what proof assistants can express and automate.

This is a fully remote, flexible contract role built for mathematicians who care deeply about precision, structure, and the future of mechanized mathematics.

• 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 systems) with an emphasis on clarity, correctness, and structural elegance
• Analyze domain-specific and general proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that probe and push the limits of existing proof assistants --- especially where tools struggle or fail
• Collaborate with AI 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 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 where automated provers break down --- whether due to complexity, missing lemmas, or insufficient libraries
• Uncover deeper patterns and generalizations implicit in the original mathematics through Lean formalization

Who You Are

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
• 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 dense, informal arguments into clean, structured formal proofs
• Comfortable working independently and managing your own time across flexible hours

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 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 cutting-edge AI projects alongside leading research labs
• Fully remote and flexible --- work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually rich work
• Operate at the true frontier of formal verification and AI reasoning research
• Potential for ongoing work and contract extension as new projects launch