Applied Formal Methods Researcher (Lean 4)
About this role
About the Role What if your deep mathematical training could directly shape how AI reasons about proofs — pushing the boundaries of what machines can verify, understand, and automate? We're looking for mathematicians with hands-on experience in formal proof systems to translate rigorous human arguments into machine-verifiable Lean 4 formalizations. You'll work at the cutting edge of AI research, helping map the frontier of automated reasoning and formal verification. This is a fully remote, flexible contract role designed for mathematically mature problem-solvers who find satisfaction in the precise, structural beauty of formal proof. - 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 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
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