Remote Researcher: Lean 4 & Formal Proofs for AI

Alignerr Corp.; Auckland; Remote; NZD 83,000 - 152,000; Part time

Job summary

Alignerr is seeking researchers to translate informal mathematics into Lean 4 and related proof systems. You will analyze, formalize, and extend proofs, probing the limits of proof assistants while collaborating with peers to improve verification pipelines.

The role emphasizes deep mathematical training, a passion for formal verification, and the ability to express complex reasoning in machine-verifiable form. This is a fully remote hourly contract, offering flexible hours.

Qualifications

• Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems - Lean strongly preferred.

Responsibilities

• Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 (and related proof systems).
• Analyze proofs across domains - identifying gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that probe 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 clean, readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques.
• Investigate where automated provers fail - and articulate precisely why (complexity, missing lemmas, library gaps, etc.).
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics.

Skills

Proof writing

Formal verification

Abstract reasoning

Collaboration

Education

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

Tools

Lean 3/4

Coq

Isabelle/HOL

Agda

Job description

Alignerr is seeking researchers to translate informal mathematics into Lean 4 and related proof systems. You will analyze, formalize, and extend proofs, probing the limits of proof assistants while collaborating with peers to improve verification pipelines.

The role emphasizes deep mathematical training, a passion for formal verification, and the ability to express complex reasoning in machine-verifiable form. This is a fully remote hourly contract, offering flexible hours.