Researcher - Lean 4 & Formal Proof Systems

What You'll Do

• Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations
• Analyze proofs across domains — algebra, analysis, topology, logic, discrete math — identifying hidden assumptions, gaps, and formalizable sub-structures
• Create formalizations that stress-test the limits of existing proof assistants, especially where automation breaks down
• Collaborate with researchers to design and refine 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
• Investigate where automated provers fail — and articulate precisely why (complexity, missing lemmas, library gaps, etc.)
• Create Lean proofs that surface 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 one or more of: 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 4 strongly preferred
• Be deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal mathematical arguments into precise, structured formal proofs
• Be intellectually energized by working at the frontier — where tools struggle and human insight still matters most

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
• Prior exposure to theorem provers where automated reasoning frequently requires manual scaffolding
• Background in data annotation, data quality, or evaluation systems
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to collaborators