Lean 4 Proof Engineer — Mathematical Formalization (AI Training)
About The Role
What if your deep mathematical expertise could directly shape the future of AI reasoning? We're looking for Lean 4 Proof Engineers to formalize advanced mathematical arguments into machine-verifiable proofs — working at the very frontier of what modern proof assistants can express, capture, and automate.
This is a fully remote, flexible contract role built for mathematicians who live at the intersection of rigorous proof construction and formal verification. If you find genuine satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can understand, this role was designed 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 emphasis on clarity, structure, and correctness
Analyze generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that test the limits of existing proof assistants, especially where automated tools struggle or fail
Collaborate with AI 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
Formalize classical proofs and compare machine-verifiable structures against textbook arguments
Investigate where automated provers break down — and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.)
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
Possess 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 formal systems — with 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, and machine-checkable formalizations
Comfortable working independently with precision and intellectual rigor
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, data quality, or AI evaluation systems
Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
Work on cutting-edge AI projects alongside world-leading research labs
Fully remote and flexible — work when and where it suits you
Freelance autonomy with the structure of meaningful, intellectually stimulating work
Get direct exposure to how advanced AI models are trained and evaluated on mathematical reasoning
Contribute to mapping the frontier of what formal verification can achieve
Potential for ongoing work and contract extension as new projects launch