Applied Formal Methods Researcher (Lean 4)

About The Role

What if your deep mathematical training could directly shape how AI reasons, proves, and understands the world's hardest problems? 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 for mathematicians who are passionate about formal verification and want their expertise to matter at the frontier of mechanized mathematics.

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: 10–40 hours/week
  
  

What You'll Do

• Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations
• Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that stress-test the limits of existing proof assistants, especially where automation breaks down
• Investigate why automated provers fail — whether due to complexity, missing lemmas, or insufficient libraries — and articulate your findings clearly
• 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
• Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments
• Reveal deeper patterns or generalizations implicit in existing mathematical arguments
  
  

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 formal systems — Lean 4 strongly preferred
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense informal arguments into clean, precise formal proofs with clarity and structure
• A mathematically mature problem-solver who finds satisfaction in resolving gaps that automated tools cannot yet bridge
  
  

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, evaluation systems, or data quality workflows
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
  
  

Why Join Us

• Work on cutting-edge AI projects 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 exposure to advanced LLMs and how frontier AI systems are trained and evaluated
• Contribute to work that genuinely advances the state of mechanized mathematics and AI reasoning
• Potential for ongoing work and contract extension as new projects launch