Remote Lean 4 Proof Engineer — Mathematical Formalization for AI

Alignerr Corp.; Sheffield (TX); Remote; USD 83,000 - 165,000; Part time

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to translate informal mathematical arguments into machine-verifiable Lean formalizations for AI research. You’ll tackle proofs beyond current automation and contribute to the future of mechanized mathematics in a fully remote setting.

Ideal candidates hold a strong math background, proven proof-writing skills, and hands-on experience with Lean, Coq, or Isabelle/HOL.

Qualifications

• Master's degree or higher in Mathematics, Logic, or Theoretical Computer Science
• Strong foundation in rigorous proof writing across 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 strongly preferred
• Deeply enthusiastic about formal verification and mechanized mathematics
• Able to translate dense informal arguments into precise formal proofs with minimal ambiguity
• Self-directed and comfortable working independently in an asynchronous, remote environment

Responsibilities

• 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
• Construct formalizations that test and extend the limits of existing proof assistants—especially where automation fails
• Investigate where automated provers break down and articulate the underlying reasons (complexity, missing lemmas, library gaps, etc.)
• Collaborate with AI researchers to design, refine, and evaluate formal verification strategies
• Provide expert guidance on proof decomposition, lemma selection, and structuring approaches
• Develop proof scripts that reveal deeper patterns or generalizations implicit in the original mathematics
• Compare machine-verifiable structures against classical textbook arguments to surface new insights

Skills

Mathematics

Formal verification

Proof writing

Independent work

Asynchronous work

Education

Master's degree

Tools

Lean 3

Lean 4

Coq

Isabelle/HOL

Agda

Job description

Alignerr is seeking a Lean 4 Proof Engineer to translate informal mathematical arguments into machine-verifiable Lean formalizations for AI research. You’ll tackle proofs beyond current automation and contribute to the future of mechanized mathematics in a fully remote setting.

Ideal candidates hold a strong math background, proven proof-writing skills, and hands-on experience with Lean, Coq, or Isabelle/HOL.