Remote Lean 4 Proof Engineer — Mathematical Formalization

Alignerr Corp.; Sheffield (TX); Remote; USD 83,000 - 193,000; Full time

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to translate advanced mathematical arguments into machine-checkable Lean proofs for AI training. This is a remote, flexible hourly contract designed for mathematically mature problem-solvers who value precision, structure, and explicit formalization.

You'll work with AI researchers to identify gaps, develop reusable proof scripts, and push the limits of current proof assistants.

Qualifications

• Master's degree or higher in Mathematics, Logic, or related field.
• Strong proof-writing and mathematical maturity across algebra, analysis, topology, logic.
• Hands-on experience with Lean 3 or Lean 4; Coq, Isabelle/HOL, or Agda preferred.

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

Proof theory

Lean proof writing

Formal verification

Mathematics

Proof analysis

Education

Master's degree or higher in Mathematics or closely related field

Tools

Lean (Lean 3/4)

Coq

Isabelle/HOL

Job description

Alignerr is seeking a Lean 4 Proof Engineer to translate advanced mathematical arguments into machine-checkable Lean proofs for AI training. This is a remote, flexible hourly contract designed for mathematically mature problem-solvers who value precision, structure, and explicit formalization.

You'll work with AI researchers to identify gaps, develop reusable proof scripts, and push the limits of current proof assistants.