Mathematical Formalization Specialist

Mathematical Formalization Specialist (Lean / Formal Proof Systems)

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.

About The Role

• 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