Mathematical Formalization Specialist

Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About The Role

What if your deep mathematical expertise could directly shape the future of AI reasoning? We're looking for mathematicians with formal verification experience to translate advanced human-written proofs into machine-verifiable Lean formalizations --- working at the very edge of what proof assistants can do today.

This is a fully remote, flexible contract role designed for mathematicians who find genuine satisfaction in precision, structure, and pushing the limits of mechanized reasoning.

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

What You'll Do

• Translate informal mathematical proofs into Lean (Lean 3 or Lean 4) with a focus on clarity, correctness, and structural elegance
• Analyze proofs across domains --- identifying hidden assumptions, logical gaps, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants
• Collaborate with AI researchers to design and refine formal verification strategies
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
• Investigate where automated provers break down and articulate why --- helping map the frontier of formal verification

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 (strongly preferred), Coq, Isabelle/HOL, Agda, or a comparable formal proof system
• Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
• Able to take a dense, informal mathematical argument and express it precisely in a form a machine can verify
• Self-directed and comfortable working independently on complex, open-ended problems

Nice to Have

• Familiarity with type theory, the Curry--Howard correspondence, or proof automation tools
• Experience contributing to large-scale formalization projects such as mathlib
• Exposure to theorem provers in settings where automation frequently fails or requires manual scaffolding
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Sample Work

• Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments
• Identify and articulate precisely where and why automated provers fail --- missing lemmas, library gaps, complexity barriers
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics

Why Join Us

• Work on genuinely cutting-edge AI research alongside leading labs --- your contributions directly advance AI reasoning
• Fully remote and asynchronous --- work when and where it suits you
• Freelance autonomy with meaningful, intellectually stimulating task-based work
• Rare opportunity to work at the intersection of advanced mathematics and frontier AI development
• Potential for ongoing work and contract extension as new formalization projects launch