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Lean Proof Engineer - Mathematical Formalization
Job Description & How to Apply Below
Location: Montreal
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
- 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
- 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
- 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
- Work on genuinely frontier problems at the intersection of mathematics and AI
- Collaborate with world-leading AI research teams and labs
- Fully remote and flexible — 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
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