Lean 4 Proof Engineer — Mathematical Formalization (AI Training)

About The Role

What if your mathematical expertise could directly shape how the world's most advanced AI systems reason, prove, and understand mathematics? We're looking for Lean 4 Proof Engineers to translate rigorous human-written arguments into machine-verifiable formal proofs — working at the very edge of what automated reasoning can do today.

This is a fully remote, flexible contract role built for mathematicians who live and breathe formal verification. You'll work on proofs that push past the limits of current automated provers, collaborating with leading AI research teams on problems that genuinely matter.

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

What You'll Do

- Translate informal mathematical proofs into clean, correct, machine-verifiable Lean 4 formalizations
- Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable substructures
- Construct formalizations that stress-test the boundaries of proof assistants, especially where automation breaks down
- Collaborate with AI researchers to design and refine formal verification strategies and pipelines
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
- Advise on proof decomposition, lemma selection, and structuring techniques for complex formal models
- Investigate and articulate where automated provers fail — whether due to complexity, missing lemmas, or library gaps
- Surface deeper patterns or generalizations hidden within classical proofs through formalization

Who You Are

- Master's degree or higher in Mathematics, Logic, Theoretical Computer Science,



or a closely related field
- Deep 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 strongly preferred), Coq, Isabelle/HOL, Agda, or comparable systems
- Genuinely excited by formal verification, proof assistants, and the future of mechanized mathematics
- Able to take dense, informal arguments and express them with the precision a machine can verify

Nice to Have

- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
- Experience contributing to or navigating large-scale formalization projects such as Mathlib
- Exposure to theorem provers in contexts where automated reasoning frequently fails or requires manual scaffolding
- Prior work in data annotation, quality evaluation, or AI training workflows
- Strong communication skills for documenting formalization decisions, edge cases, and proof strategies

The Ideal Candidate You're a mathematically mature problem-solver who finds genuine satisfaction in taking a dense, elegant argument and expressing it in a form that a machine can understand and verify. You appreciate precision and structural beauty — and you're energized, not discouraged, by the gaps that automated tools cannot yet bridge.

Why Join Us

- Work directly with world-leading AI research labs on problems at the frontier of formal mathematics
- Fully remote and adaptable — work when and where it suits you
- Freelance autonomy with the structure of meaningful, technically demanding work
- Gain exposure to how cutting-edge large language models are trained and evaluated on mathematical reasoning
- Potential for ongoing work and contract extension as new projects launch

📌 Lean 4 Proof Engineer - Mathematical Formalization (Australia)
🏢 Alignerr
📍 Australia