Remote Lean 4 Proof Architect

Alignerr Corp.; Seattle (WA); Remote; USD 83,000 - 165,000; Part time

Job summary

Alignerr Corp. seeks a Formal Verification Scientist to translate advanced proofs into machine-verifiable Lean formalizations.

This fully remote, hourly contract role is ideal for mathematicians who operate at the intersection of rigorous proof and cutting-edge computer science. You'll work on translating informal arguments into structured proofs, analyze gaps, and test proof assistants’ limits, collaborating with AI researchers to refine verification pipelines.

Qualifications

• Master’s degree or higher in mathematics, logic, or a closely related field.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems.
• Ability to translate dense informal mathematical arguments into clean, structured proofs.
• Strong foundation in rigorous proof writing across algebra, analysis, topology, logic, or discrete math.

Responsibilities

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with emphasis on clarity and correctness.
• Analyze generic and domain-specific proofs, identifying gaps and formalizable sub-structures.
• Construct formalizations that test the limits of existing proof assistants, especially where automation struggles.
• Collaborate with AI researchers to design and evaluate strategies for improving formal verification pipelines.
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof idioms.
• Provide 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 due to complexity or missing libraries.
• Create Lean proofs that reveal deeper patterns or generalizations in the original mathematics.

Skills

Proof writing

Formal verification

Mathematical maturity

Communication

Education

Master’s degree or higher in Mathematics/Logic/CS

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

Alignerr Corp. seeks a Formal Verification Scientist to translate advanced proofs into machine-verifiable Lean formalizations.

This fully remote, hourly contract role is ideal for mathematicians who operate at the intersection of rigorous proof and cutting-edge computer science. You'll work on translating informal arguments into structured proofs, analyze gaps, and test proof assistants’ limits, collaborating with AI researchers to refine verification pipelines.