Formal Verification Scientist (Lean 4 & Mathlib)

Formal Verification Scientist (Lean 4 & Mathlib)

About the Role

What if your deep mathematical training could directly shape how AI understands and reasons about formal proofs? We're looking for Formal Verification Scientists to translate rigorous human mathematics into machine-verifiable Lean 4 proofs — working at the very edge of what modern proof assistants can express and automate.

This is a fully remote, flexible contract role for mathematicians who love precision, structural elegance, and the challenge of pushing formal systems to their limits.

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

What You'll Do

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility
• Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants, particularly where automation struggles or fails
• Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines
• Investigate where and why automated provers break down — complexity, missing lemmas, library gaps — and document your findings clearly
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
• Create Lean proofs that reveal 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
• Strong foundation 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 systems — Lean 4 strongly preferred
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
• Ability to take dense, elegant human arguments and express them in precise, machine-verifiable form
• Self-directed and comfortable working independently on complex, open-ended problems

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 significant manual scaffolding
• Prior experience with data annotation, data quality, or AI evaluation workflows
• Strong written communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work directly on cutting-edge AI research projects alongside leading AI labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually demanding work
• Operate at the frontier of formal verification and AI — where very few people in the world can contribute
• Potential for ongoing work and contract extension as new projects launch