Remote Lean 4 Formal Methods Researcher

Alignerr Corp.; Birmingham; Remote; GBP 69,000 - 103,000; Part time

Job summary

Alignerr is seeking Applied Formal Methods Researchers to translate rigorous human mathematical arguments into Lean 4 formalizations — supporting machine-verifiable proofs at the frontier of automated reasoning. This fully remote, flexible contract role is designed for mathematicians who love precision, structure, and the challenge of bridging human intuition with machine-verifiable logic.

Responsibilities include translating informal proofs into Lean 4, analyzing proofs for gaps, constructing

Qualifications

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

Responsibilities

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with emphasis on clarity, structure, and correctness.
• Analyze proofs across domains—identifying gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that test and expose the limits of existing proof assistants.
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
• Develop 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.
• Investigate breakdowns in automated provers and articulate why they occur—complexity, missing lemmas, insufficient libraries.
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments.

Skills

Formal verification enthusiasm

Independent working

Clear communication

Education

Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field

Tools

Lean 4

Lean 3

Coq

Isabelle/HOL

Agda

Job description

Alignerr is seeking Applied Formal Methods Researchers to translate rigorous human mathematical arguments into Lean 4 formalizations — supporting machine-verifiable proofs at the frontier of automated reasoning. This fully remote, flexible contract role is designed for mathematicians who love precision, structure, and the challenge of bridging human intuition with machine-verifiable logic.

Responsibilities include translating informal proofs into Lean 4, analyzing proofs for gaps, constructing