Researcher - Lean 4 & Formal Proof Systems

- 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 proofs across domains — 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 researchers to design, refine, and evaluate strategies for improving formal verification pipelines * Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms * Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models * Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond * Create Lean proofs that reveal 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 math * Have 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 * Able to translate informal mathematical arguments into clean, structured formal proofs independently * Naturally precise, patient, and driven by structural elegance and logical completeness

Nice to Have

* Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools * Experience with 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 workflows * Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

* Work on cutting-edge AI projects alongside leading research labs and top AI teams * Fully remote and flexible — work when and where it suits you * Freelance autonomy with the structure of meaningful, intellectually stimulating work * Operate at the true frontier of formal verification and mechanized mathematics * Contribute directly to how next-generation AI systems reason about mathematics and logic * Potential for ongoing work and contract extension as new projects launch