Researcher - Lean 4 & Formal Proof Systems

What You'll Do

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with a focus on clarity, structure, and correctness
• Analyze domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Create formalizations that test and extend the limits of existing proof assistants — especially where automated tools struggle or fail
• 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 and articulate precisely why — complexity, missing lemmas, insufficient libraries, and beyond
• 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
• 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 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 clean, structured formal proofs
• Be a mathematically mature problem-solver who finds genuine 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 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