Lean 4 Proof Engineer - Mathematical Formalization
Posted Today by Alignerr
Negotiable
Undetermined
Remote
Birmingham, England, United Kingdom
Summary: The Lean 4 Proof Engineer role involves translating rigorous mathematical proofs into machine-verifiable formalizations using Lean 4, focusing on correctness and clarity. This fully remote contract position is ideal for mathematicians passionate about formal verification and mechanized mathematics. Candidates will analyze proofs, construct formalizations, and collaborate with AI researchers to enhance verification pipelines. The role offers flexibility in hours and the opportunity to work on cutting-edge problems in AI and mathematics.
Key Responsibilities:
- Translate informal mathematical proofs into clean, structured Lean 4 formalizations.
- Analyze proofs to identify hidden assumptions, logical gaps, and formalizable substructures.
- Construct formalizations that probe and stress-test the limits of existing proof assistants.
- Investigate breakdowns in automated provers and articulate reasons for failures.
- Collaborate with AI researchers to design and refine formal verification pipelines.
- Create Lean proofs that reveal deeper patterns or generalizations in original mathematics.
- Compare machine-verifiable structures against classical textbook arguments.
Key Skills:
- Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a related field.
- Experience in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics.
- Hands-on experience with Lean (preferably Lean 4).
- Excitement about formal verification and proof assistants.
- Ability to convert dense mathematical arguments into structured formal proofs.
- Self-directed and comfortable working independently in an asynchronous environment.
- Familiarity with Coq, Isabelle/HOL, Agda, or other interactive theorem provers (nice to have).
- Knowledge of type theory and proof automation tools (nice to have).
- Experience with large-scale formalization projects and AI training pipelines (nice to have).
- Strong written communication skills for documenting formalization decisions.
Salary (Rate): £140.00 hourly
City: Birmingham
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 how the world's most advanced AI systems reason about proofs? We're looking for Lean 4 Proof Engineers to translate rigorous mathematical arguments into machine-verifiable formalizations — working at the very edge of what modern proof assistants can express and automate. This is a fully remote, flexible contract role designed for mathematicians who care about precision, structure, and the future of mechanized mathematics.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
- Translate informal mathematical proofs into clean, structured Lean 4 formalizations — with a focus on correctness, clarity, and reproducibility
- Analyze proofs across domains to identify hidden assumptions, logical gaps, and formalizable substructures
- Construct formalizations that probe and stress-test the limits of existing proof assistants
- Investigate where automated provers break down — and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.)
- Collaborate with AI researchers to design and refine formal verification pipelines
- Apply expert judgment in proof decomposition, lemma selection, and structuring strategies
- Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
- Compare machine-verifiable structures against classical textbook arguments
Who You Are
- Holder of a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Rigorous proof writer with deep experience across areas such as algebra, analysis, topology, logic, or discrete mathematics
- Hands-on practitioner with Lean (Lean 3 or Lean 4), with strong preference for Lean 4 experience
- Genuinely excited about formal verification, proof assistants, and the frontier of mechanized mathematics
- Able to take dense, informal mathematical arguments and render them into precise, structured formal proofs
- Self-directed and comfortable working independently in an asynchronous environment
Nice to Have
- Familiarity with Coq, Isabelle/HOL, Agda, or other interactive theorem provers
- Knowledge of type theory, the Curry-Howard correspondence, and proof automation tools
- Experience contributing to large-scale formalization projects such as Mathlib
- Exposure to contexts where automated reasoning regularly fails or requires significant manual scaffolding
- Prior experience with data annotation, evaluation systems, or AI training pipelines
- Strong written communication skills for documenting formalization decisions, edge cases, and proof strategies
Why Join Us
- Work directly with leading AI research labs on some of the most technically demanding problems in formal mathematics
- Fully remote and flexible — structure your hours to fit your life
- Freelance autonomy with the depth and purpose of meaningful, frontier-level work
- Rare opportunity to work where mathematics, computer science, and AI training genuinely intersect
- Potential for ongoing work and contract extension as new projects launch