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 proofs — pushing the boundary of what machines can understand and verify? We're looking for mathematicians and formal verification specialists to translate sophisticated human‑written arguments into precise, machine‑checkable Lean 4 proofs for cutting‑edge AI research. This is a fully remote, flexible contract role designed for researchers who thrive on rigor, structure, and working at the frontier of mechanized mathematics.

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

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, correctness, and structural elegance
• Analyze domain‑specific proofs to identify gaps, hidden assumptions, and formalizable sub‑structures
• Construct formalizations that probe the limits of existing proof assistants — especially where automation breaks down
• Collaborate with AI 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 expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers fail and articulate why — complexity, missing lemmas, insufficient libraries, or structural issues
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics

• 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 systems — Lean 4 strongly preferred
• Able to translate informal mathematical arguments into clean, structured formal proofs
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics

• Familiarity with type theory, the Curry‑Howard correspondence, and proof automation tooling
• 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

• Work on cutting‑edge AI research alongside leading labs and research teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually demanding work
• Contribute directly to advancing what AI can understand, verify, and reason about in mathematics
• Potential for ongoing work and contract extension as new projects launch