Mathematical Formalization Specialist

Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About the Role

What if your mathematical expertise could directly shape how AI reasons, proves, and understands the most complex ideas in human knowledge? We're looking for mathematicians with formal verification experience to translate advanced mathematical arguments into machine-verifiable proofs — working at the very frontier of what AI and proof assistants can do.

This is a fully remote, flexible contract role built for mathematicians who love precision, structure, and the challenge of expressing rigorous ideas in a form that machines can verify and learn from.

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: Flexible — work on your own schedule

What You'll Do

• Translate informal mathematical proofs into Lean (or related proof systems) with an emphasis on clarity, correctness, and structure
• Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants, especially where automation 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 proof assistant idioms
• Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and more

Who You Are

• Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Possess 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 proof systems — Lean strongly preferred
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal mathematical arguments into clean, structured formal proofs

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 explaining formalization decisions, edge cases, and proof strategies

The Ideal Candidate

You're a mathematically mature problem-solver who finds genuine satisfaction in taking a dense, elegant human argument and expressing it in a form that a machine can understand and verify. You appreciate precision and structural beauty — and you're energized by the challenge of resolving the gaps that automated tools cannot yet bridge.

Sample Work

• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Identify exactly where and why automated provers fail — and document those boundaries clearly
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

Why Join Us

• Work on cutting-edge AI projects alongside leading AI research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually rigorous work
• Contribute directly to advancing the reliability and reasoning capabilities of AI at the frontier
• Potential for ongoing work and contract extension as new projects launch