Remote Researcher: Lean 4 & Formal Proofs

Alignerr Corp.; Ireland; Remote; EUR 83,000 - 124,000; Full time

Job summary

Alignerr is seeking a Researcher to translate informal proofs into Lean 4 and related proof systems for AI training in mechanized mathematics. This remote hourly contract focuses on rigorous formalization and clear, machine-verifiable proofs across mathematical domains.

Candidate will analyze proofs, test automation boundaries, and collaborate to refine verification pipelines while contributing to advanced AI-driven formal reasoning research.

Qualifications

• Master's degree or higher in Mathematics, Logic, or Theoretical Computer Science.
• Strong proof writing and mathematical reasoning across algebra, analysis, topology, logic, or discrete math.
• Experience with Lean, Coq, Isabelle/HOL, or comparable systems.
• Ability to translate informal proofs into machine-verifiable formal proofs.
• Interest in AI training for formal reasoning and mechanized mathematics.

Responsibilities

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with emphasis on clarity, structure, and correctness.
• Analyze proofs across domains to identify gaps, assumptions, and formalizable sub-structures.
• Construct formalizations that test the limits of existing proof assistants.
• Investigate where automated provers break down due to complexity or missing libraries.
• Develop readable, reproducible proof scripts aligned with best practices and idioms.
• Collaborate with researchers to design strategies for improving formal verification pipelines.
• Provide guidance on proof decomposition, lemma selection, and structure for formal models.
• Formalize classical proofs and compare machine-verifiable structures with textbook arguments.
• Surface deeper patterns or generalizations implicit in the original mathematics.

Skills

Mathematics

Logic

Theoretical Computer Science

Proof writing

Education

Master's degree or higher in Mathematics, Logic, Theoretical Computer Science

Tools

Lean (Lean 3/Lean 4)

Coq

Isabelle/HOL

Agda

Job description

Alignerr is seeking a Researcher to translate informal proofs into Lean 4 and related proof systems for AI training in mechanized mathematics. This remote hourly contract focuses on rigorous formalization and clear, machine-verifiable proofs across mathematical domains.

Candidate will analyze proofs, test automation boundaries, and collaborate to refine verification pipelines while contributing to advanced AI-driven formal reasoning research.