Applied Formal Methods Researcher Lean 4

About The Role

What if your deep mathematical training could directly shape how AI reasons about the hardest problems in mathematics? We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — working at the exact boundary where human mathematical intuition meets machine-verifiable logic.

This is a fully remote, flexible contract role for mathematicians who are passionate about formal verification and excited to push the limits of what proof assistants can do.

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

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, structure, and correctness
• Analyze domain-specific and general proofs, identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test 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 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
• Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, or otherwise
• Reveal deeper patterns and generalizations implicit in the original mathematics through your formalizations
  
  

• Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Strong foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof systems — Lean 4 strongly preferred
• Able to translate informal mathematical arguments into clean, structured formal proofs
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• A mathematically mature problem-solver who finds satisfaction in expressing elegant human arguments in a form a machine can verify
  
  

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

• Work on cutting-edge AI projects alongside leading research labs and AI teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually challenging work
• Contribute directly to the development of AI systems that can reason about advanced mathematics
• Work at the true frontier of formal verification — on problems that push the limits of what machines can understand
• Potential for ongoing work and contract extension as new projects launch