Applied Formal Methods Researcher (Lean 4)
Posted Today by Alignerr
Negotiable
Undetermined
Remote
Birmingham, England, United Kingdom
Summary: The role of Applied Formal Methods Researcher focuses on translating informal mathematical proofs into machine-verifiable formalizations using Lean 4. This fully remote position is tailored for mathematicians who excel in precision and structural elegance, aiming to bridge human intuition with automated reasoning. The researcher will engage in analyzing proofs, constructing formalizations, and collaborating with peers to enhance formal verification processes. The position offers flexible hours and the opportunity to work at the forefront of AI research.
Key Responsibilities:
- Translate informal mathematical proofs into Lean 4 with an emphasis on clarity, structure, and correctness.
- Analyze proofs across domains, identifying gaps, hidden assumptions, and formalizable sub-structures.
- Construct formalizations that test and expose the limits of existing proof assistants.
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
- Develop readable, reproducible proof scripts aligned with mathematical best practices.
- Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
- Investigate breakdowns in automated provers and articulate reasons for their occurrence.
- Formalize classical proofs and compare machine-verifiable structures against textbook arguments.
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 proof systems.
- Enthusiastic about formal verification, proof assistants, and mechanized mathematics.
- Able to translate informal mathematical arguments into structured, machine-verifiable proofs.
- Detail-oriented, precise, and comfortable working independently.
- 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 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 Applied Formal Methods Researchers to translate rigorous human mathematical arguments into machine-verifiable Lean 4 formalizations — working at the very frontier of what automated reasoning can express and achieve. This is a fully remote, flexible contract role designed for mathematicians who love precision, structural elegance, and the intellectual challenge of bridging human intuition with machine-verifiable logic.
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 proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test and expose the limits of existing proof assistants, especially where automated tools struggle or fail
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Develop 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
- Investigate breakdowns in automated provers and articulate why they occur — complexity, missing lemmas, insufficient libraries, and more
- Formalize classical proofs and compare machine-verifiable structures against textbook arguments
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 proof systems — Lean 4 strongly preferred
- Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate informal mathematical arguments into clean, structured, machine-verifiable proofs
- Naturally detail-oriented, precise, and comfortable working independently
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 evaluation, or AI training workflows
- Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work at the cutting edge of AI research alongside world-leading research labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually stimulating work
- Gain direct exposure to how advanced AI models are trained and evaluated
- Contribute to a field that is actively redefining the boundaries of mathematical reasoning and AI capability
- Potential for ongoing work and contract extension as new projects launch