Formal Verification Scientist (Lean 4 & Mathlib)
Posted Today by Alignerr
Negotiable
Undetermined
Remote
Birmingham, England, United Kingdom
Summary: The role of Formal Verification Scientist involves translating advanced mathematical arguments into machine-verifiable Lean 4 proofs, contributing to the development of AI's understanding of formal proof. This fully remote contract position is ideal for mathematicians who enjoy rigorous proof construction and tackling significant problems. Candidates will work on the cutting edge of proof assistants, enhancing formal verification pipelines and collaborating with researchers. The position offers flexible hours and the opportunity to engage in meaningful, technically demanding work.
Key Responsibilities:
- Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4.
- Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures.
- Construct formalizations that push the limits of existing proof assistants.
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms.
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
- Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
- Investigate where automated provers break down and articulate reasons for failures.
- Create Lean proofs that surface 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 and mathematical reasoning.
- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable formal system.
- Enthusiasm for formal verification, proof assistants, and mechanized mathematics.
- Able to translate informal arguments into clean, structured, formally correct proofs.
- Mathematically mature problem-solver with an appreciation for precision and structural beauty.
- 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 and reasoning strategies.
Salary (Rate): £170.00 hourly
City: Birmingham
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 understands and reasons about formal proof? We're looking for Formal Verification Scientists to translate advanced mathematical arguments into machine-verifiable Lean 4 proofs — working at the very frontier of what proof assistants can express, capture, and automate. This is a fully remote, flexible contract role built for mathematicians who love rigorous proof construction and want to work on problems that matter. If you find satisfaction in taking a dense, elegant human 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 precise, machine-verifiable formalizations in Lean 4
- Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that push the limits of existing proof assistants — especially where automated tools struggle or fail
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Investigate where automated provers break down and clearly articulate why — complexity, missing lemmas, insufficient libraries, and beyond
- Create Lean proofs that surface 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
- Strong foundation in rigorous proof writing and mathematical reasoning 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 a comparable formal system — Lean strongly preferred
- Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate informal arguments into clean, structured, formally correct proofs
- Mathematically mature problem-solver who appreciates precision, structural beauty, and the challenge of bridging gaps automated tools can't yet close
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 leading research labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, technically demanding work
- Contribute directly to how AI systems learn to reason about advanced mathematics
- Exposure to frontier LLM research and how formal verification intersects with AI training
- Potential for ongoing work and contract extension as new projects launch