About The Role

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

This is a fully remote, flexible contract role for mathematicians who live and breathe rigorous proof construction and are passionate about pushing the limits of formal verification.

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

What You'll Do

Translate informal mathematical proofs into Lean 4 with a strong emphasis on clarity, correctness, and structural elegance Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures Construct formalizations that test the limits of existing proof assistants — especially where automation breaks down or fails Collaborate with researchers to design and refine strategies for improving formal verification pipelines Develop readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models Formalize classical proofs and compare machine-verifiable structures against textbook arguments Investigate and articulate where automated provers fail — whether due to complexity, missing lemmas, or insufficient libraries Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics

Who You Are

Holder of a 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 Experienced with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean is strongly preferred Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics Able to translate informal, human-written arguments into clean, precise, structured formal proofs A mathematically mature problem-solver who finds deep satisfaction in expressing elegant arguments in forms a machine can verify

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 requires manual scaffolding Prior experience with data annotation, data quality, or evaluation systems Strong communication skills for documenting formalization decisions, edge cases, and reasoning strategies

Why Join Us

Work on cutting-edge AI projects alongside the world's leading research labs Fully remote and flexible — work when and where it suits you Freelance autonomy with intellectually stimulating, high-impact work Contribute directly to expanding the frontier of what formal verification can capture and automate Potential for ongoing work and contract extension as new projects launch