Applied Formal Methods Researcher (Lean 4)
Posted 1 day ago by Alignerr
Negotiable
Undetermined
Remote
Cambridge, England, United Kingdom
Summary: The role of Applied Formal Methods Researcher focuses on translating informal mathematical proofs into machine-verifiable formalizations using Lean 4, contributing to AI research and formal verification. This fully remote contract position is ideal for mathematicians passionate about proof assistants and aims to have a significant impact on the future of AI. The role requires collaboration with AI researchers and emphasizes clarity, structure, and correctness in formal proofs. 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 domain-specific and general proofs to identify gaps, hidden assumptions, and formalizable sub-structures.
- Construct formalizations that probe the limits of existing proof assistants.
- Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices.
- Provide expert guidance on proof decomposition, lemma selection, and structuring techniques.
- Investigate where automated provers break down and articulate reasons for failures.
- Formalize classical proofs and reveal deeper patterns or generalizations 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 various mathematical areas.
- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems.
- Enthusiastic about formal verification and proof assistants.
- Able to translate complex informal arguments into structured formal proofs.
- Mathematically mature and comfortable working independently.
- 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).
- Strong communication skills for explaining formalization decisions and proof strategies.
Salary (Rate): £170.00/hr
City: Cambridge
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 the foundations of mathematics? We're looking for Applied Formal Methods Researchers to translate rigorous human-written proofs into machine-verifiable formalizations in Lean 4 — working at the cutting edge of AI research and formal verification. This is a fully remote, flexible contract role designed for mathematicians who are passionate about proof assistants and want their expertise to have a real, lasting impact on the future of 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 systems) with an emphasis on clarity, structure, and correctness
- Analyze domain-specific and general proofs to identify gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that probe the limits of existing proof assistants — especially where automated tools struggle or fail
- Collaborate with AI 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 — whether due to complexity, missing lemmas, or insufficient libraries
- Formalize classical proofs and 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 formal systems — Lean strongly preferred
- Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate complex informal arguments into clean, structured, and correct formal proofs
- Mathematically mature and comfortable working independently at the frontier of what proof assistants can express
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
- Prior exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
- Background in data annotation, data quality, or evaluation systems
- Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to collaborators
Why Join Us
- Work directly 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 depth and meaning of frontier research
- Contribute to work that is actively shaping the future of mathematical reasoning in AI
- Potential for ongoing engagement and contract extension as new projects launch