Remote Formal Verification Scientist - Lean 4 & Mathlib

Alignerr Corp.; Cambridge; Remote; GBP 55,000 - 124,000; Full time

Job summary

Alignerr is seeking a Formal Verification Scientist to translate advanced mathematics into machine-verifiable knowledge using Lean 4 and related systems. This fully remote, hourly contract role targets mathematicians who enjoy rigorous proof and mechanized mathematics.

You will contribute to proving and formalizing complex arguments, collaborating with researchers to enhance verification pipelines, and producing readable proof scripts in Lean idioms.

Qualifications

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

Responsibilities

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with 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 where automated tools struggle or fail.
• 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 Lean 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 — complexity, missing lemmas, insufficient libraries, and more.
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics.

Skills

Lean 4

Formal proofs

Mathematics

Education

Master's degree in Mathematics or related

Tools

Coq

Isabelle/HOL

Lean 4

Job description

Alignerr is seeking a Formal Verification Scientist to translate advanced mathematics into machine-verifiable knowledge using Lean 4 and related systems. This fully remote, hourly contract role targets mathematicians who enjoy rigorous proof and mechanized mathematics.

You will contribute to proving and formalizing complex arguments, collaborating with researchers to enhance verification pipelines, and producing readable proof scripts in Lean idioms.