Applied Formal Methods Researcher (Lean 4)

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 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 for formal models * Investigate where automated provers break down — and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.) * Formalize classical proofs and compare machine-verifiable structures against textbook arguments

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 a comparable formal proof system — Lean strongly preferred * Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics * Able to translate complex informal arguments into clean, structured formal proofs independently * Thrive working at the frontier — you're energized by problems that automated tools can't yet solve

Nice to Have

* Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools * Experience contributing to large-scale formalization projects (e.g., mathlib) * Exposure to theorem provers where automated reasoning frequently requires manual scaffolding * Prior experience with data annotation, evaluation systems, or AI training workflows * Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

* Work directly with leading AI research labs on cutting-edge projects at the intersection of mathematics and AI * Fully remote and flexible — work when and where it suits you * Freelance autonomy with meaningful, intellectually stimulating work * Gain exposure to advanced LLMs and the training pipelines that shape them * Contribute to work that defines the future of mechanized mathematics and AI reasoning * Potential for ongoing work and contract extension as new projects launch