Lean 4 Proof Engineer — Mathematical Formalization

About The Role

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

We're looking for mathematicians and formal verification specialists to translate rigorous mathematical arguments into machine-verifiable Lean 4 proofs for cutting-edge AI research. This role sits at the frontier of mathematics and computer science, where human intuition meets the precision of formal proof systems.

This is a fully remote, flexible contract role — ideal for someone who finds genuine satisfaction in the challenge of expressing elegant mathematical arguments in a form a machine can verify.

- 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
- Work at the frontier of formal verification, constructing proofs that test or exceed the current capabilities of automated provers
- Investigate where automated provers break down and articulate why — missing lemmas, complexity limits, insufficient libraries
- Collaborate with researchers to design and refine strategies for improving formal verification pipelines
- Guide proof decomposition, lemma selection, and structuring techniques for formal models
- Formalize classical proofs and compare machine-verifiable structures against textbook arguments




- Develop 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
- 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 assistants — Lean 4 strongly preferred
- Able to translate dense informal arguments into clean, structured formal proofs
- Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics

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

Why Join Us

- Work on genuinely frontier problems at the intersection of mathematics and AI
- Collaborate with world-leading AI research teams and labs
- Fully remote and adaptable — work when and where it suits you
- Freelance autonomy with the structure and intellectual depth of meaningful research-adjacent work
- Gain exposure to how advanced AI models are trained and evaluated
- Potential for ongoing work and contract extension as projects evolve

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