Researcher - Lean 4 & Formal Proof Systems
About this role
About the Role What if your deep mathematical training could directly shape how AI reasons about formal proofs — pushing the boundaries of what machines can verify, understand, and automate? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs for cutting-edge AI research. This is rare, high-impact work at the intersection of mathematics and computer science — and you'll be working on problems that sit beyond the current reach of automated provers. - Organization: Alignerr - Type: Hourly Contract - Location: Remote - Commitment: 10–40 hours/week What You'll Do - Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 (and related proof systems), with a focus on clarity, correctness, and structure - Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures - Construct formalizations that test and expand 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 strategies for formal models - Investigate where and why automated provers break down — articulating failure modes around complexity, missing lemmas, or library gaps - 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 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 systems — Lean is strongly preferred - Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics - Able to take a dense, human-written mathematical argument and express it cleanly in a form a machine can verify - Self-directed and rigorous — you find satisfaction in resolving the 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 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 on genuinely frontier problems in formal verification and AI research - Collaborate with teams at the cutting edge of AI and mathematical reasoning - Fully remote and async-friendly — work on your own schedule, from anywhere - Freelance autonomy: choose your hours, maintain your independence - Exposure to how advanced AI models are trained and evaluated on mathematical reasoning - Potential for ongoing work and contract extension as new projects launch
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