Lean 4 Proof Engineer - Mathematical Formalization
Posted Today by Alignerr
Negotiable
Undetermined
Remote
London, England, United Kingdom
Summary: The Lean 4 Proof Engineer role focuses on translating advanced mathematical arguments into machine-verifiable Lean 4 proofs, bridging human intuition with machine precision. This fully remote contract position seeks mathematically mature problem-solvers to work on the cutting edge of formal verification and AI. Candidates will analyze proofs, collaborate with AI researchers, and develop structured formalizations. The role offers flexibility in hours and the opportunity to contribute to significant AI research projects.
Key Responsibilities:
- Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility.
- Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures.
- Work at the limits of existing proof assistants, tackling cases where automated tools struggle or fail entirely.
- Collaborate with AI researchers to design and evaluate strategies for improving formal verification pipelines.
- Develop proof scripts aligned with mathematical best practices and proof assistant idioms.
- Provide expert guidance on proof decomposition, lemma selection, and structuring techniques.
- Investigate and articulate where and why automated provers break down — complexity, missing lemmas, library gaps, and beyond.
- Formalize classical proofs and compare machine-verifiable structures against textbook arguments.
Key Skills:
- Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
- Deep foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics.
- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal proof systems — Lean 4 strongly preferred.
- Passionate about formal verification, proof assistants, and the future of mechanized mathematics.
- Able to translate dense, informal mathematical arguments into clean, structured formal proofs.
- Appreciation for precision, structural elegance, and the challenge of resolving gaps that automated tools cannot yet bridge.
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools (nice to have).
- Experience contributing to large-scale formalization projects such as Mathlib (nice to have).
- Exposure to theorem provers in regimes where automated reasoning frequently fails or requires extensive manual scaffolding (nice to have).
- Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies (nice to have).
Salary (Rate): £170.00 hourly
City: London
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 mathematical expertise could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians and formal verification specialists to translate advanced mathematical arguments into precise, machine-verifiable Lean 4 proofs — working at the very frontier of what proof assistants can express and automate. This is a fully remote, flexible contract role for mathematically mature problem-solvers who find deep satisfaction in bridging human intuition and machine precision.
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 an emphasis on clarity, correctness, and reproducibility
- Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures
- Work at the limits of existing proof assistants, tackling cases where automated tools struggle or fail entirely
- Collaborate with AI researchers to design and evaluate strategies for improving formal verification pipelines
- Develop proof scripts aligned with mathematical best practices and proof assistant idioms
- Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
- Investigate and articulate where and why automated provers break down — complexity, missing lemmas, library gaps, and beyond
- Formalize classical proofs and compare machine-verifiable structures against textbook arguments
Who You Are
- Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Deep foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal proof systems — Lean 4 strongly preferred
- Passionate about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate dense, informal mathematical arguments into clean, structured formal proofs
- You appreciate precision, structural elegance, and the challenge of resolving gaps that automated tools cannot yet bridge
Nice to Have
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
- Experience contributing to large-scale formalization projects such as Mathlib
- Exposure to theorem provers in regimes where automated reasoning frequently fails or requires extensive manual scaffolding
- Prior experience with data annotation, evaluation systems, or AI training workflows
- Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work on cutting-edge AI research projects alongside world-leading labs
- Fully remote and flexible — structure your own hours and work from anywhere
- Freelance autonomy with access to genuinely frontier-level mathematical and AI problems
- Contribute to work that defines the boundary of what formal verification and AI can achieve together
- Potential for ongoing work and contract extension as new projects launch