Applied Formal Methods Researcher (Lean 4)
Posted Today by Alignerr
Negotiable
Outside
Remote
Edinburgh, Scotland, United Kingdom
Summary: The Applied Formal Methods Researcher role focuses on formalizing advanced mathematics in Lean 4, bridging human reasoning and machine verifiability. This fully remote contract position is ideal for mathematicians passionate about proof theory and computation. Candidates will translate informal proofs into formal structures, analyze gaps in reasoning, and collaborate on improving verification pipelines. The role offers flexibility and the opportunity to work on cutting-edge AI projects.
Key Responsibilities:
- Translate informal mathematical proofs into Lean 4 with an 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, especially where automation struggles or fails.
- 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 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 precisely why.
- 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 mathematics.
- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems, with Lean strongly preferred.
- Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics.
- Able to translate informal mathematical arguments into clean, structured formal proofs.
- Comfortable working independently in an asynchronous, remote environment.
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools (nice to have).
- Experience with large-scale formalization projects such as Mathlib (nice to have).
- Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies.
Salary (Rate): £170.00 hourly
City: Edinburgh
Country: United Kingdom
Working Arrangements: remote
IR35 Status: outside IR35
Seniority Level: Mid-Level
Industry: IT
About The Role
What if your deep mathematical training could directly shape how AI understands and constructs rigorous proofs? We're looking for Applied Formal Methods Researchers to formalize advanced mathematics in Lean 4 — working at the precise boundary where human mathematical reasoning meets machine verifiability. This is a fully remote, flexible contract role built for mathematicians who live at the intersection of proof theory and computation. If you find satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify — this role was made for you.
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 an 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, especially where automation struggles or fails
- 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 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 precisely why
- 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 mathematics
- Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean strongly preferred
- Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate informal mathematical arguments into clean, structured formal proofs
- Comfortable working independently in an asynchronous, remote environment
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, data quality, or evaluation systems
- Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work on cutting-edge AI projects alongside the world's leading AI research labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually rigorous work
- Direct impact on how AI systems learn to reason about advanced mathematics
- Exposure to state-of-the-art large language models and how they're trained on formal reasoning
- Potential for ongoing work and contract extension as new projects launch