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
- Thrive 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