Applied Formal Methods Researcher (Lean 4) in London

About The Role

What if your deep mathematical training could directly shape how AI reasons, proves, and understands mathematics at a fundamental level? We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — working at the precise intersection of rigorous mathematics and cutting-edge AI research.

About The Role

What if your deep mathematical training could directly shape how AI reasons, proves, and understands mathematics at a fundamental level? We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — working at the precise intersection of rigorous mathematics and cutting-edge AI research.

This is a fully remote, flexible contract role designed for mathematicians who are passionate about formal verification and want their expertise to matter at scale.

• Organization: Alignerr




• Type: Hourly Contract




• Location: Remote




• Commitment: 10–40 hours/week

What You'll Do

• Translate informal mathematical proofs into clean, machine-verifiable Lean 4 formalizations with an emphasis on clarity, structure, and correctness




• Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures




• Construct formalizations that probe the limits of existing proof assistants, especially where automation fails or falls short




• 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 expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models




• Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond




• 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 math




• Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof systems — Lean strongly preferred




• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics




• Able to translate informal mathematical arguments into precise, clean, structured formal proofs




• Thrives working independently and asynchronously at the frontier of a fast-moving field

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 manual scaffolding




• Prior experience with data annotation, data quality evaluation, or AI training workflows




• Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work directly with world-leading AI research teams on projects at the cutting edge of formal mathematics and AI




• Fully remote and flexible — work when and where it suits you




• Freelance autonomy with meaningful, intellectually stimulating work




• Gain rare exposure to how advanced AI models are trained to reason mathematically




• Contribute to defining the frontier of what formal verification can express, capture, and automate




• Potential for ongoing work and contract extension as new projects launch