Applied Formal Methods Researcher (Lean 4)

About The Role

What if your deep mathematical training could directly shape how AI understands and constructs rigorous proofs? We’re looking for Applied Formal Methods Researchers to formalise advanced mathematics in Lean 4 — working at the precise boundary where human mathematical reasoning meets machine verifiability.

This is a fully remote, flexible contract role built for mathematicians who live at the intersection of proof theory and computation. If you find satisfaction in taking a dense, elegant 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 Lean 4 (and related proof systems) with an emphasis on clarity, structure, and correctness
• Analyze generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test the limits of existing proof assistants, especially where automation struggles or fails
• 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 guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Formalise classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate where automated provers break down — and articulate precisely why
• Create Lean proofs that reveal deeper patterns or generalisations 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 systems — Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanised mathematics
• Able to translate informal mathematical arguments into clean, structured formal proofs
• Comfortable working independently in an asynchronous, remote environment

Nice to Have

• Familiarity with type theory, the Curry‑Howard correspondence, and proof automation tools
• Experience with large‑scale formalisation 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 formalisation decisions, edge cases, and reasoning strategies

Why Join Us

• Work 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 structure of meaningful, intellectually rigorous work
• Direct impact on how AI systems learn to reason about advanced mathematics
• Exposure to state‑of‑the‑art large language models and how they’re trained on formal reasoning
• Potential for ongoing work and contract extension as new projects launch

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