Remote Lean 4 Researcher — Formal Proof Systems

Alignerr; Charlotte (AR); On-site; USD 83,000 - 165,000; Part time

Job summary

Alignerr is seeking a Researcher to translate complex mathematical arguments into Lean 4 formalizations for AI training. You will convert informal proofs into machine-verifiable code, explore proofs across algebra, analysis, topology, logic, and discrete math, and push the boundaries where automation struggles.

This remote hourly contract offers flexible 10–40 hours per week, collaboration with researchers, and the challenge of making rigorous human reasoning legible to machines.

Qualifications

• Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Have a 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 systems — Lean 4 strongly preferred.
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics.
• Able to translate dense, informal mathematical arguments into precise, structured formal proofs.
• Intellectually energized by working at the frontier — where tools struggle and human insight still matters most

Responsibilities

• Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations.
• Analyze proofs across domains — algebra, analysis, topology, logic, discrete math — identifying hidden assumptions, gaps, and formalizable sub-structures.
• Construct formalizations that stress-test the limits of existing proof assistants, especially where automation breaks down.
• Collaborate with researchers to design and refine strategies for improving formal verification pipelines.
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
• Investigate where automated provers fail — and articulate precisely why (complexity, missing lemmas, library gaps, etc.)
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics

Skills

Formal proofs

Lean / proof assistants

Mathematics background

Translation of informal proofs

Frontier research mindset

Education

Master's degree or higher in Mathematics/Logic/Theoretical CS

Tools

Lean 3/4

Coq

Isabelle/HOL

Agda

Job description

Alignerr is seeking a Researcher to translate complex mathematical arguments into Lean 4 formalizations for AI training. You will convert informal proofs into machine-verifiable code, explore proofs across algebra, analysis, topology, logic, and discrete math, and push the boundaries where automation struggles.

This remote hourly contract offers flexible 10–40 hours per week, collaboration with researchers, and the challenge of making rigorous human reasoning legible to machines.