Applied Formal Methods Researcher (Lean 4)

Applied Formal Methods Researcher (Lean 4)

About the Role

What if your deep mathematical training could directly shape how AI understands and reasons about formal proofs? We're looking for Applied Formal Methods Researchers to translate rigorous human mathematics into machine-verifiable Lean 4 proofs — working at the very edge of what automated reasoning can do today.

This is a fully remote, flexible contract role for mathematicians who are passionate about formal verification, proof assistants, and the future of mechanized mathematics. If you find satisfaction in taking a dense, elegant argument and expressing it in a form a machine can understand, this role was built for you.

• 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 an emphasis on clarity, structure, and correctness
• Analyze both 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 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 — articulating 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 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 mechanized mathematics
• Able to translate informal mathematical arguments into clean, well-structured formal proofs
• Mathematically mature and comfortable working at the frontier of what formal verification can express

Nice to Have

• Prior experience with data annotation, data quality, or evaluation systems
• 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 requires manual scaffolding
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work on cutting-edge AI projects alongside world-leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with meaningful, intellectually rigorous work
• Contribute directly to how next-generation AI systems reason about mathematics
• Potential for ongoing work and contract extension as new projects launch