Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About The Role

What if your mathematical expertise could directly shape how AI reasons, verifies, and understands formal logic We're looking for mathematicians with deep proof-writing experience to translate complex human arguments into machine-verifiable formalizations — working at the very edge of what AI and proof assistants can do today.

This is a fully remote, flexible contract role built for mathematicians who find beauty in precision and satisfaction in solving problems that automated tools simply cannot.

Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: Flexible, task-based

What You'll Do

Translate informal mathematical proofs into Lean (and related proof systems) with a focus on clarity, structure, and correctness
Analyze generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that test and extend the limits of existing proof assistants, especially where tools struggle or fail
Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
Develop clean, readable, and reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
Investigate where automated provers break down and articulate why — surfacing patterns, missing lemmas, or library gaps

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 formal systems — Lean strongly preferred
Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Able to take a dense, elegant human argument and express it in a form a machine can understand and 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
Strong written communication skills for documenting formalization decisions, edge cases, and reasoning strategies

Why Join Us

Work on cutting-edge AI research projects alongside leading AI labs
Fully remote and asynchronous — work when and how it suits you
Freelance autonomy with the structure of meaningful, intellectually stimulating work
Contribute to a frontier discipline that is actively shaping the future of AI reliability and mathematical reasoning
Potential for ongoing work and contract extension as new formalization projects launch