Applied Formal Methods Researcher (Lean 4)

About The Role What if your deep mathematical expertise could directly shape how AI reasons, proves, and understands the world's hardest problems? We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — working at the frontier of mechanized mathematics and cutting-edge AI research. This is a fully remote, flexible contract role built for mathematicians who thrive on precision, structural elegance, and the challenge of expressing rigorous human reasoning in a form a machine can verify.

• 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 domain-specific and general proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test the limits of existing proof assistants — especially where automated tools struggle or fail
• 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
• Investigate where automated provers break down and articulate precisely why — complexity, missing lemmas, insufficient libraries, and beyond
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

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 and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete math
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean strongly preferred
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
• Ability to translate informal arguments into clean, structured, machine-verifiable formal proofs
• A mathematically mature problem-solver who finds satisfaction in resolving gaps that 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 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 directly with leading AI research labs on some of the most intellectually demanding problems in formal mathematics
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, high-impact technical work
• Contribute to defining the frontier of what AI can reason about and formally verify
• Potential for ongoing work and contract extension as new projects launch