Researcher - Lean 4 & Formal Proof Systems

Researcher — Lean 4 & Formal Proof Systems (AI Training)

About the Role

What if your deep mathematical expertise could directly shape how AI reasons about formal proofs — pushing the frontier of what machines can understand and verify?

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 role sits at the intersection of mathematics and computer science, working on problems that lie beyond the reach of current automated provers.

This is a fully remote, flexible contract role built for researchers who love rigor, precision, and the challenge of expressing elegant human reasoning in a form a machine can trust.

• 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 domain-specific and general mathematical arguments — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants, especially where automation breaks down
• Investigate failure modes in automated provers and articulate precisely why they occur — complexity barriers, missing lemmas, insufficient libraries
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Collaborate with researchers to design and refine strategies for improving formal verification pipelines
• Create Lean proofs that reveal deeper patterns or generalizations implicit in original mathematical arguments
• Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models

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 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 formal proof systems — Lean 4 strongly preferred
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
• Ability to take dense, informal arguments and express them in clean, structured, machine-verifiable form
• Self-directed and comfortable working at the frontier, where the right path isn't always obvious

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 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 research projects in collaboration with leading AI labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually demanding work
• Contribute directly to expanding what AI can understand and verify in advanced mathematics
• Potential for ongoing work and contract extension as new projects launch