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

About The Role

What if your deep mathematical training could directly shape the future of AI — and push the boundaries of what machines can reason about and verify?

We're looking for mathematicians and formal methods specialists to translate sophisticated human-written proofs into machine-verifiable Lean 4 formalizations.

This is frontier work: you'll be operating at the edge of what automated provers can currently handle, helping map the limits of formal verification and contributing to some of the most technically demanding AI research happening today.

This is a fully remote, versátil contract role designed for mathematically mature researchers who love rigor, structure, and the intellectual challenge of bridging human reasoning and mechanized proof.

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

What You'll Do

- Translate informal mathematical proofs into precise, machine-verifiable Lean 4 formalizations — with an emphasis on clarity, structure, and correctness
- Analyze proofs across domains (algebra, analysis, topology, logic, discrete math) to identify hidden assumptions, gaps, and formalizable sub-structures
- Construct formalizations that test and expose the limits of existing proof assistants — especially where automation breaks down
- Develop clean, readable, reproducible proof scripts aligned with best practices and Lean idioms
- Provide expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models
- Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines
- Investigate where automated provers fail and articulate why — whether due to complexity, missing lemmas,



library gaps, or fundamental limitations
- Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics

Who You Are

- Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Have a strong foundation in rigorous proof writing and mathematical reasoning across at least one of: algebra, analysis, topology, logic, or discrete mathematics
- Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable proof assistant — Lean 4 strongly preferred
- Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Able to take a dense, elegant human argument and express it in a form a machine can verify — with precision and structural care

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 significant manual scaffolding
- Prior experience with data annotation, evaluation systems, or AI training workflows
- Strong written communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

- Work at the frontier of formal verification alongside teams building cutting-edge AI systems
- Fully remote and flexible — structure your work around your schedule, anywhere in the world
- Freelance autonomy with meaningful, intellectually rigorous task-based work
- Direct exposure to how advanced AI models are trained and evaluated on mathematical reasoning
- Potential for ongoing work and contract extension as new projects launch

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