Applied Formal Methods Researcher (Lean 4)
Posted Today by Alignerr
Negotiable
Undetermined
Remote
Glasgow, Scotland, United Kingdom
Summary: The Applied Formal Methods Researcher role focuses on translating complex mathematical proofs into machine-verifiable formalizations, utilizing Lean 4 and related proof systems. This fully remote contract position is ideal for mathematicians passionate about rigorous proof construction and automated reasoning. The role involves collaboration with AI researchers to enhance formal verification pipelines and contribute to cutting-edge AI projects. Candidates should possess a strong mathematical background and experience with formal systems.
Key Responsibilities:
- Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4.
- Analyze proofs across domains to identify hidden assumptions, logical gaps, and formalizable sub-structures.
- Construct formalizations that test and expose the limits of existing proof assistants.
- Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines.
- Develop clean, readable, and reproducible proof scripts aligned with mathematical best practices.
- Guide proof decomposition strategies, including lemma selection and formal modeling decisions.
- Investigate breakdowns in automated provers and articulate reasons for failures.
- Create Lean proofs that reveal deeper patterns and generalizations in 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.
- Enthusiasm for formal verification, proof assistants, and mechanized mathematics.
- Able to translate dense mathematical arguments into structured formal proofs.
- Mathematically mature with a focus on resolving gaps in automated tools.
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools (nice to have).
- Experience with large-scale formalization projects and theorem provers (nice to have).
- Strong written communication skills for explaining formalization decisions.
Salary (Rate): £140.00 hourly
City: Glasgow
Country: United Kingdom
Working Arrangements: remote
IR35 Status: undetermined
Seniority Level: undetermined
Industry: IT
About The Role
What if your mathematical expertise could directly shape how AI reasons about the hardest problems in mathematics? We're looking for Applied Formal Methods Researchers to translate complex human-written proofs into machine-verifiable formalizations — working at the very frontier of what automated reasoning can do. This is a fully remote, flexible contract role designed for mathematicians who live and breathe rigorous proof construction and want to apply that expertise to one of the most exciting challenges in modern AI.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
- Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 (and related proof systems)
- Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures
- Construct formalizations that test and expose the limits of existing proof assistants
- Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines
- Develop clean, readable, and reproducible proof scripts aligned with mathematical best practices
- Guide proof decomposition strategies — including lemma selection, structuring techniques, and formal modeling decisions
- Investigate where automated provers break down and articulate why — whether due to complexity, missing lemmas, or library gaps
- Create Lean proofs that surface deeper patterns and 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 strongly preferred
- Deeply enthusiastic about formal verification, proof assistants, and the long-term potential of mechanized mathematics
- Able to translate dense, informal mathematical arguments into clean, structured formal proofs
- Mathematically mature — you find genuine satisfaction in 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 where automated reasoning frequently fails or requires extensive manual scaffolding
- Prior experience with data annotation, data quality evaluation, or AI training workflows
- Strong written communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work on cutting-edge AI projects alongside world-leading research labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually challenging work
- Contribute directly to advancing the frontier of AI mathematical reasoning
- Potential for ongoing work and contract extension as new projects launch
- Global collaboration with a team at the intersection of mathematics and AI