Lean 4 Proof Engineer - Mathematical Formalization

About the Role

What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for Lean 4 Proof Engineers to formalize advanced mathematical proofs for cutting-edge AI research — working at the precise intersection where rigorous mathematics meets machine-verifiable logic. This is a fully remote, flexible contract role built for mathematicians who find genuine satisfaction in translating elegant human arguments into structures a machine can understand and verify. If you live for precision and thrive at the frontier of what formal proof assistants can do, this role was made for you.

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

Responsibilities

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with a focus on clarity, structure, and correctness
• Analyze generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that push the limits of existing proof assistants, especially where 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
• Guide proof decomposition, lemma selection, and structuring strategies 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 surface deeper patterns or generalizations implicit in the original mathematics

Requirements

• 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 systems — Lean strongly preferred
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
• Ability to translate informal mathematical arguments into clean, well-structured formal proofs
• Self-motivated and capable of working independently in an asynchronous, remote environment

Nice to Have

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
• Experience contributing to large-scale formalization projects (e.g., Mathlib)
• Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
• Prior experience with data annotation, data quality, or evaluation systems
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Benefits

• Work directly on cutting-edge AI projects alongside world-leading research labs
• Fully remote and async-friendly — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Contribute to mapping the frontier of what formal verification can express, capture, and automate
• Gain rare exposure to how advanced AI models are trained and evaluated at the highest level
• Potential for ongoing work and contract extension as new projects launch