Researcher - Lean 4 & Formal Proof Systems

Overview

Researcher - Lean 4 & Formal Proof Systems te and formalize advanced mathematical proofs in Lean for cutting-edge AI research. Ideal for mathematicians passionate about formal verification and pushing the limits of modern proof assistants.

• Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness.
• Analyze generic and domain-specific proofs, identifying gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that test the limits of existing proof assistants, especially where tools struggle or fail.
• Collaborate with 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.
• 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, and articulate why (e.g., complexity, missing lemmas, insufficient libraries).
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics.

• Master’s degree (or higher) in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean (Lean 3 or Lean
  4), Coq, Isabelle/HOL, Agda, or comparable systems, with Lean strongly preferred.
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics.
• Ability to translate informal arguments into clean, structured formal proofs.

• Prior experience with data annotation, data quality, or evaluation systems.
• Familiarity with type theory, Curry-Howard correspondence, and proof automation tools.
• Experience with large-scale formalization projects (e.g., mathlib).
• Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding.
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies.
• A mathematically mature problem-solver who enjoys taking dense human arguments and expressing them so a machine can understand.

• Competitive pay and flexible remote work.
• Exposure to advanced LLMs and how they’re trained.
• Freelance perks: autonomy, flexibility, and global collaboration.
• Potential for contract extension.

• Type:
  Hourly Contract
• Location:
  
  Remote
• Commitment: 10–40 hours/week
• About the company:
  
  Alignerr
• Application process:
  
  Submit resume, complete a short screening, project matching and onboarding

Application notes:
Our team reviews applications daily. Please complete your AI interview and application steps to be considered for this opportunity.