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

About The Role

What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical proofs into Lean 4 — working at the exact boundary where human mathematical intuition meets machine-verifiable logic.

This is a fully remote, flexible contract role designed for researchers who love rigor, structure, and pushing the limits of what proof assistants can do. If you find satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify, this role was built for you.

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

What You'll Do

- Translate informal mathematical proofs into Lean 4 (and related proof systems) with a strong emphasis on clarity, structure, and correctness
- Analyze domain-specific and general proofs to identify gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test the limits of existing proof assistants — especially where tools struggle or fail
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Develop highly 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 break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond




- Create Lean proofs that reveal deeper patterns or generalizations implicit in original mathematical arguments

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 across algebra, analysis, topology, logic, or discrete mathematics
- Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean strongly preferred
- Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate informal mathematical arguments into clean, structured, machine-verifiable formal proofs
- Mathematically mature and comfortable working at the frontier of what formal verification can currently express

Nice to Have

- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
- Experience with 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, data quality, or AI evaluation systems
- Robust communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

- Work directly on cutting-edge AI research projects alongside leading AI labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually rigorous work
- Contribute to advancing what AI systems can reason about mathematically
- Potential for ongoing work and contract extension as new research projects launch
- Collaborate with a global team of researchers working at the frontier of AI and formal mathematics

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