Mathematical Formalization Specialist

Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About the Role

What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems to translate advanced mathematical arguments into machine-verifiable formalizations — working at the very edge of what proof assistants can do today.

This is a fully remote, flexible contract role built for mathematicians who love precision, structural elegance, and the challenge of expressing rigorous human reasoning in a form a machine can understand.

• 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, correctness, and structure
• Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable sub-structures
• Construct formalizations that test the limits of existing proof assistants, particularly where automated tools struggle or fail
• Collaborate with AI researchers to design and refine formal verification strategies
• Develop clean, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Guide proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate automated prover failure modes and articulate why they occur

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 proof assistants — Lean strongly preferred
• Genuinely excited about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal mathematical arguments into precise, structured formal proofs
• 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 (e.g., mathlib)
• Exposure to theorem provers where automated reasoning frequently requires manual scaffolding
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies

Sample Work

• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate where automated provers break down and document why — 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 projects alongside leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Contribute directly to advancing the frontier of formal verification and AI mathematical reasoning
• Potential for ongoing work and contract extension as new projects launch