Applied Formal Methods Researcher (Lean 4)
Posted 1 day ago by Alignerr
Negotiable
Undetermined
Remote
London, England, United Kingdom
Summary: The Applied Formal Methods Researcher role focuses on formalizing advanced mathematical proofs in Lean 4, bridging rigorous mathematics and AI research. This fully remote contract position is ideal for mathematicians passionate about formal verification, allowing them to contribute to significant projects in the field. Candidates will translate informal proofs into machine-verifiable formats and collaborate with researchers to enhance formal verification processes. The role offers flexibility in hours and location, catering to independent and asynchronous work styles.
Key Responsibilities:
- Translate informal mathematical proofs into clean, machine-verifiable Lean 4 formalizations with an emphasis on clarity, structure, and correctness.
- Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures.
- Construct formalizations that probe the limits of existing proof assistants, especially where automation fails or falls short.
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms.
- Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
- Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond.
- Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics.
Key Skills:
- Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
- Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete math.
- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof systems — Lean strongly preferred.
- Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics.
- Able to translate informal mathematical arguments into precise, clean, structured formal proofs.
- Ability to thrive working independently and asynchronously at the frontier of a fast-moving field.
- 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 where automated reasoning frequently fails or requires manual scaffolding (nice to have).
- Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies.
Salary (Rate): £140.00 hourly
City: London
Country: United Kingdom
Working Arrangements: remote
IR35 Status: undetermined
Seniority Level: undetermined
Industry: IT
About The Role
What if your deep mathematical training could directly shape how AI reasons, proves, and understands mathematics at a fundamental level? We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — working at the precise intersection of rigorous mathematics and cutting-edge AI research. This is a fully remote, flexible contract role designed for mathematicians who are passionate about formal verification and want their expertise to matter at scale.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
- Translate informal mathematical proofs into clean, machine-verifiable Lean 4 formalizations with an emphasis on clarity, structure, and correctness
- Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that probe the limits of existing proof assistants, especially where automation fails or falls short
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
- Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond
- Create Lean proofs that reveal 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
- Possess a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete math
- Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof systems — Lean strongly preferred
- Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate informal mathematical arguments into precise, clean, structured formal proofs
- Thrive working independently and asynchronously at the frontier of a fast-moving field
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 where automated reasoning frequently fails or requires manual scaffolding
- Prior experience with data annotation, data quality evaluation, or AI training workflows
- Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work directly with world-leading AI research teams on projects at the cutting edge of formal mathematics and AI
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with meaningful, intellectually stimulating work
- Gain rare exposure to how advanced AI models are trained to reason mathematically
- Contribute to defining the frontier of what formal verification can express, capture, and automate
- Potential for ongoing work and contract extension as new projects launch