Researcher - Lean 4 & Formal Proof Systems

Researcher – Lean 4 & Formal Proof Systems

About the Role

What if your deep mathematical expertise could directly shape how the next generation of AI understands and reasons about formal proof? We're looking for mathematicians and formal verification specialists to translate rigorous human-written proofs into machine-verifiable formalizations in Lean 4 — working at the very frontier of what proof assistants can express and automate.

This is a fully remote, flexible contract role built for mathematically mature researchers who thrive at the intersection of mathematics and computer science.

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: 10–40 hours/week

What You'll Do

• 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
• Construct formalizations that test and push the limits of existing proof assistants, especially in areas where automation struggles or fails
• Investigate where automated provers break down and articulate why — whether due to complexity, missing lemmas, or insufficient libraries
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

Who You Are

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Strong foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean 4 strongly preferred
• Able to translate dense, informal mathematical arguments into clean, structured formal proofs
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics

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 significant manual scaffolding
• Prior experience with data annotation, data quality, or AI evaluation workflows
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to collaborators

Why Join Us

• Work alongside world-leading AI research teams on genuinely cutting-edge projects
• Fully remote and flexible — structure your hours around your life, not the other way around
• Freelance autonomy with the intellectual depth of meaningful, high-impact research work
• Gain direct exposure to how advanced AI models are trained and evaluated on formal mathematics
• Contribute to mapping the frontier of what formal verification can capture and automate
• Potential for ongoing work and contract extension as new projects launch