Applied Formal Methods Researcher (Lean 4)

About The Role

What if your deep mathematical training could directly shape how AI reasons, proves, and thinks? We're looking for formal methods researchers to translate complex human mathematical arguments into machine-verifiable proofs in Lean 4 — working at the precise frontier where human ingenuity meets the limits of automated reasoning.

This is a fully remote, flexible contract role built for mathematicians who live at the intersection of rigorous proof construction and the future of mechanized mathematics.

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

What You'll Do

• Translate informal mathematical proofs into formal, machine-verifiable Lean 4 proofs with an emphasis on clarity, correctness, and structural elegance
• Analyze domain-specific and general proofs to identify hidden assumptions, logical gaps, and formalizable sub-structures
• Construct challenging formalizations that probe the limits of current proof assistants — especially where automation breaks down
• Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines
• Develop clean, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
• Investigate failure modes in automated provers and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and beyond
• Create formalizations that surface deeper patterns or generalizations implicit in the original mathematics
  
  

Who You Are

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Deeply fluent in rigorous proof writing 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 assistants — Lean strongly preferred
• Genuinely passionate about formal verification, proof assistants, and the long-term future of mechanized mathematics
• Able to bridge the gap between intuitive human arguments and precise formal representations
  
  

Nice to Have

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling
• Experience contributing to large-scale formalization projects such as Mathlib
• Exposure to theorem provers where automated reasoning frequently fails or requires substantial manual scaffolding
• Prior experience with data annotation, data quality evaluation, or AI training workflows
• Strong ability to communicate formalization decisions, edge cases, and reasoning strategies clearly in writing
  
  

Why This Role Stands Out

This isn't routine annotation work. You'll operate at the cutting edge — tackling proofs that automated systems cannot yet handle, mapping the frontier of what formal verification can express, and contributing directly to how next-generation AI models learn to reason mathematically. If you find deep satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify, this role was built for you.

Why Join Us

• Work on genuinely frontier AI research alongside leading labs
• Fully remote and asynchronous — work on your own schedule, from anywhere
• Freelance autonomy with meaningful, intellectually stimulating work
• Contribute to shaping how AI models understand and generate formal mathematics
• Potential for contract extension as projects evolve and expand