Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About The Role

What if your deep mathematical training could directly shape how AI reasons, verifies, and understands formal logic? We're looking for expert mathematicians to translate advanced human-written proofs into machine-verifiable formalizations — working at the exact boundary of what modern proof assistants can and cannot yet do.

This is a fully remote, flexible contract role built for mathematicians who are passionate about rigorous proof construction and formal verification. If you find satisfaction in taking a dense, elegant argument and expressing it with the precision a machine can verify, this role was made for you.

Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: Flexible

What You'll Do

Translate informal mathematical proofs into Lean (and related proof systems) with a focus on clarity, structure, and correctness Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures Construct formalizations that push the limits of existing proof assistants, especially where automation breaks down Collaborate with researchers to design and refine strategies for improving formal verification pipelines Develop clean, readable, and reproducible proof scripts aligned with mathematical best practices Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models Investigate and articulate why automated provers fail on specific problems — complexity, missing lemmas, insufficient libraries, or otherwise

Who You Are

Hold 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 Have hands-on experience with Lean (Lean 3 or Lean 4) — or comparable systems like Coq, Isabelle/HOL, or Agda — with Lean strongly preferred Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics Able to translate informal arguments into well-structured, machine-verifiable proofs with minimal scaffolding

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 proving contexts where automated reasoning frequently requires manual intervention Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to collaborators

Sample Tasks

Formalize classical proofs and compare machine-verifiable structures against textbook arguments Identify where automated provers break down and document why — feeding directly into AI research Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics

Why Join Us

Work at the frontier of AI research alongside leading labs advancing model reasoning and reliability Fully remote and asynchronous — work when and where it suits you Freelance autonomy with the structure of meaningful, high-impact technical work Your expertise directly shapes the next generation of AI formal reasoning capabilities Potential for ongoing work and contract extension as new projects launch