Formal Verification Scientist (Lean 4 & Mathlib)

What if your deepest mathematical expertise could directly shape how AI understands and reasons about formal proof? We're looking for Formal Verification Scientists to translate advanced human-written mathematics into machine-verifiable Lean 4 proofs — working at the frontier of what proof assistants can currently express, capture, and automate. This is a fully remote, flexible contract role for mathematicians who love rigorous proof construction and want their work to matter at the cutting edge of AI research.

Responsibilities

• Translate informal mathematical proofs into precise, machine-verifiable Lean 4 formalizations with an emphasis on clarity, structure, and correctness
• Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
• Push the limits of existing proof assistants by constructing formalizations 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 Lean idioms
• Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate breakdowns in automated provers and articulate root causes — missing lemmas, library gaps, complexity barriers
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

Requirements

• 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
• Bring hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean 4 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Skilled at translating informal mathematical arguments into clean, well-structured formal proofs
• A mathematically mature problem-solver who finds satisfaction in expressing elegant human arguments in forms a machine can verify

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, evaluation systems, or AI training data workflows
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Benefits

• Work directly on cutting-edge AI research projects alongside leading labs and research teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with meaningful, intellectually stimulating task-based work
• Gain exposure to advanced large language models and how they are trained on formal mathematics
• Collaborate with a global team of researchers and domain experts pushing the boundaries of AI
• Potential for ongoing work and contract extension as new projects launch

Schedule

10–40 hours/week