Lean 4 Proof Engineer - Mathematical Formalization

Toronto, Ontario, Canada
Remote
Posted Oct 8, 2026
1 position

US$170–US$200 / hour

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Employment type: Contract
Experience level: Mid-level · 2+ years
Minimum education: Master’s degree
Posting language: English
Working hours: 40 hours per week
Location requirements: Country, Toronto, Ontario, Canada
Seniority: Entry level

Job summary

Translate informal mathematical arguments into clear, correct, machine-verifiable Lean 4 proofs, identifying gaps and structuring formalizations with appropriate lemmas. Collaborate with researchers to improve formal verification pipelines, investigate limitations in automated proving, and develop readable, reproducible proof scripts.

Job details

Lean 4 Proof Engineer — Mathematical Formalization About The Role What if your mathematical expertise could directly shape how AI understands and reasons about formal proof? We're looking for skilled mathematicians to translate rigorous human arguments into machine-verifiable Lean 4 formalizations — working at the very frontier of what proof assistants can express, capture, and automate. This is a fully remote, flexible contract role built for mathematicians who care deeply about formal verification and want their work to matter at the cutting edge of AI research. 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 generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures Construct formalizations that push the limits of existing proof assistants — especially where automation fails or falls short Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines Develop readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models Investigate where automated provers break down and articulate precisely why — complexity, missing lemmas, library gaps, and beyond Create Lean proofs that reveal 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 across areas such as algebra, analysis, topology, logic, or discrete mathematics Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof systems — Lean strongly preferred Deeply 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 — cleanly and completely 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, data quality, or evaluation systems Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies Why Join Us Work on genuinely frontier AI research alongside leading labs and research teams Fully remote and flexible — work when and where it suits you Freelance autonomy with the structure of intellectually stimulating, high-impact work Contribute directly to expanding what formal verification can express and automate Potential for ongoing work and contract extension as new projects launch

What you’ll do

Requirements

A master's degree or higher in mathematics, logic, theoretical computer science, or a related field is required, along with strong rigorous proof-writing skills. Hands-on experience with Lean or another proof system is expected, with Lean preferred, as well as enthusiasm for formal verification and the ability to formalize complex mathematical arguments.