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 boundaries of what machines can verify, understand, and automate? We're looking for mathematicians and formal verification researchers to translate sophisticated mathematical arguments into rigorous, machine-verifiable Lean 4 proofs. This is frontier work: you'll be operating at the edge of what proof assistants can currently do, helping map the limits of mechanized mathematics and contributing to cutting-edge AI research. This is a fully remote, flexible contract role designed for researchers who thrive on precision, structure, and intellectual challenge.
• Organization: Alignerr
• Type: Hourly Contract
•

Location:
Remote
• Commitment: 10–40 hours/week

What You'll Do
• Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility
• Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that probe the limits of existing proof assistants, especially in areas where automation breaks down
• 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 Lean idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers fail — and articulate precisely why (complexity, missing lemmas, library gaps, etc.)




• Create Lean proofs that surface 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 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 proof systems — Lean 4 strongly preferred
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
• Ability to translate dense, informal arguments into precise, structured formal proofs
• Mathematically mature and comfortable working at the frontier — where tools struggle and human insight is essential 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 in contexts where automated reasoning frequently requires manual scaffolding
• Prior experience with data annotation, quality evaluation, or AI training workflows
• Solid communication skills for articulating formalization decisions, edge cases, and reasoning strategies Why Join Us
• Work on some of the most intellectually demanding problems in AI and formal mathematics
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with meaningful, high-impact research tasks
• Collaborate with researchers at the forefront of AI development
• Gain direct exposure to how advanced AI models are trained and evaluated
• Potential for ongoing work and contract extension as new projects launch

📌 Researcher - Lean 4 & Formal Proof Systems (Sydney)
🏢 Alignerr
📍 Sydney