Lean 4 Proof Engineer - Mathematical Formalization
Posted 1 day ago by Alignerr
Negotiable
Undetermined
Remote
Manchester, England, United Kingdom
Summary: The Lean 4 Proof Engineer role focuses on translating informal mathematical proofs into machine-verifiable formalizations using Lean 4. This position requires expertise in formal verification and aims to address complex problems that automated tools cannot solve. The role is fully remote and offers flexible hours, catering to mathematically skilled individuals who appreciate precision in their work. Candidates will collaborate with researchers to enhance formal verification methodologies and contribute to the advancement of AI and mathematics.
Key Responsibilities:
- Translate informal mathematical proofs into Lean 4 with clarity, structure, and correctness.
- Analyze generic and domain-specific proofs to identify gaps and formalizable sub-structures.
- Construct formalizations that test the limits of existing proof assistants.
- Collaborate with researchers to improve formal verification pipelines.
- Develop readable, reproducible proof scripts aligned with mathematical best practices.
- Provide guidance on proof decomposition and structuring techniques for formal models.
- Investigate breakdowns in automated provers and articulate reasons for failures.
- Formalize classical proofs and compare machine-verifiable structures against textbook arguments.
- Uncover deeper patterns or generalizations implicit in the original mathematics.
Key Skills:
- Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a related field.
- Strong foundation in rigorous proof writing across various mathematical areas.
- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or similar formal systems.
- Passionate about formal verification and mechanized mathematics.
- Able to translate informal arguments into structured, machine-verifiable proofs.
- Familiarity with type theory and proof automation tools (nice to have).
- Experience with large-scale formalization projects and theorem provers (nice to have).
- Strong communication skills for explaining formalization decisions.
Salary (Rate): £170.00 hourly
City: Manchester
Country: United Kingdom
Working Arrangements: remote
IR35 Status: undetermined
Seniority Level: undetermined
Industry: IT
Lean 4 Proof Engineer — Mathematical Formalization
About The Role
What if your deep mathematical training could directly shape the future of AI — and push the boundaries of what machines can reason about? We're looking for mathematicians with formal verification expertise to translate rigorous human-written proofs into machine-verifiable Lean 4 formalizations. This role sits at the frontier of mathematics and computer science, working on problems that often lie beyond the reach of automated provers. You'll help map — and expand — what formal verification can express, capture, and automate. This is a fully remote, flexible contract role designed for mathematically mature problem-solvers who find beauty in precision and satisfaction in resolving what automated tools cannot yet bridge.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
- Translate informal mathematical proofs into Lean 4 (and related proof systems) with clarity, structure, and correctness
- Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test the limits of existing proof assistants — especially where current 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 proof assistant idioms
- Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Investigate where automated provers break down and articulate precisely why — complexity, missing lemmas, insufficient libraries, and beyond
- Formalize classical proofs and compare machine-verifiable structures against textbook arguments
- Uncover deeper patterns or generalizations implicit in the original mathematics
Who You Are
- 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 areas such as algebra, analysis, topology, logic, or discrete mathematics
- Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean 4 strongly preferred
- Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate informal arguments into clean, structured, machine-verifiable proofs
Nice to Have
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
- Experience with large-scale formalization projects such as Mathlib
- Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
- Prior experience with data annotation, evaluation systems, or AI training workflows
- Strong communication skills for explaining formalization decisions, edge cases, and proof strategies
Why Join Us
- Work on genuinely frontier problems at the intersection of mathematics and AI
- Collaborate with leading AI research teams pushing the state of the art in formal reasoning
- Fully remote and flexible — structure your work around your life
- Freelance autonomy with access to some of the most intellectually demanding problems in the field
- Exposure to advanced LLMs and how formal mathematics is used to train and evaluate them
- Potential for contract extension as new projects launch