Researcher - Lean 4 & Formal Proof Systems

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

About The Role

What if your mathematical expertise could directly shape how AI reasons about formal proofs — pushing the boundary 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 proofs, working on problems that sit at the very frontier of what automated systems can handle today.

This is a fully remote, flexible contract role designed for researchers who love rigor, structure, and the intellectual challenge of making the implicit explicit.

• 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)
• Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants, especially where automation struggles or fails
• Investigate the breakdown points of automated provers and articulate the underlying reasons — complexity, missing lemmas, library gaps, and more
• Collaborate with research teams 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 guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics

Who You Are

• Holds a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Deeply grounded in rigorous proof construction across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Experienced with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean strongly preferred
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal mathematical arguments into clean, structured, formally verified proofs
• Finds 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 fails or requires manual scaffolding
• Prior experience with data annotation, data quality, or evaluation systems
• Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work directly on cutting-edge AI research projects alongside leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with meaningful, intellectually stimulating work at the frontier of formal mathematics
• Gain rare exposure to how advanced AI models are trained on formal reasoning tasks
• Potential for ongoing work and contract extension as new projects launch