Remote Lean 4 Proof Architect for Formalization

Alignerr; United States; On-site; USD 83,000 - 165,000; Part time

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to translate informal mathematics into machine-verifiable Lean proofs. This remote, hourly contract role offers flexible hours (10–40 per week) and the chance to push the boundaries of formal verification across diverse mathematical domains.

You will develop structured Lean formalizations, audit proofs for gaps or assumptions, and collaborate with researchers to advance proof strategies and automated reasoning tools.

Qualifications

• Master's degree or higher in Mathematics, Logic, or a related field.
• Strong foundation in rigorous proof writing across algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or similar proof systems — Lean 4 preferred.

Responsibilities

• Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations.
• Analyze proofs across domains, identifying gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that test and extend the limits of existing proof assistants.
• Investigate where automated provers break down and articulate the underlying reasons.
• Collaborate with researchers to design and refine formal verification strategies.
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques.
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments.
• Create Lean proofs that reveal deeper patterns or generalizations in the original mathematics.

Skills

Lean 4

Formal verification

Mathematics

Proof writing

Education

Master's degree or higher in Mathematics

Tools

Lean 4

Coq/Isabelle/Agda

Job description

Alignerr is seeking a Lean 4 Proof Engineer to translate informal mathematics into machine-verifiable Lean proofs. This remote, hourly contract role offers flexible hours (10–40 per week) and the chance to push the boundaries of formal verification across diverse mathematical domains.

You will develop structured Lean formalizations, audit proofs for gaps or assumptions, and collaborate with researchers to advance proof strategies and automated reasoning tools.