About The Role

What if your deep mathematical training could directly shape how AI reasons about proofs — and push the boundaries of what machines can verify? We're looking for Formal Verification Scientists to translate advanced mathematical arguments into precise, machine-checkable Lean 4 formalizations, working at the very frontier of AI research and mechanized mathematics.

This is a fully remote, flexible contract role for mathematicians who love rigorous proof construction and want their expertise to matter beyond the academy.

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 and correctness Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures Push the limits of existing proof assistants, especially in areas where automated tools struggle or fail entirely Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines Develop highly 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 Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, or deeper structural issues Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

Who You Are

Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field Have 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 proof assistants — Lean strongly preferred Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics Able to translate dense, informal arguments into clean, structured formal proofs with precision and care A mathematically mature problem-solver who finds genuine 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 in settings where automated reasoning frequently fails or requires manual scaffolding Prior experience with data annotation, data quality evaluation, or AI training workflows Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

Work directly on cutting-edge AI projects alongside leading research labs Fully remote and flexible — work when and where it suits you Freelance autonomy with meaningful, intellectually stimulating work Contribute to some of the most challenging open problems at the intersection of mathematics and AI Potential for ongoing work and contract extension as new projects launch