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 (Australia)
🏢 Alignerr
📍 Australia