Mathematical Formalization Specialist

About the Role

We're looking for mathematicians with hands-on experience in formal proof systems to help us map the frontier of machine-verifiable mathematics — working on problems that automated tools simply cannot yet solve on their own. This is a fully remote, flexible contract role built for mathematicians who are passionate about precision, formal verification, and the future of mechanized reasoning.

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

Responsibilities

• Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness
• Analyze generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test the limits of existing proof assistants, especially where automated tools struggle or fail
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop highly 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 why — complexity, missing lemmas, library gaps, and more

Requirements

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof systems — Lean strongly preferred
• Genuine enthusiasm for formal verification, proof assistants, and mechanized mathematics
• Ability 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 communication skills for explaining formalization decisions, edge cases, and proof strategies

Sample Work

• Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments
• Build Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
• Document where and why existing proof assistants fall short — and help advance the tools that will bridge those gaps

Benefits

• Work at the frontier of AI research alongside leading AI labs and research teams
• Fully remote and flexible — work on your own schedule, from anywhere
• Freelance autonomy with the structure of meaningful, intellectually stimulating tasks
• Contribute to high-integrity AI datasets that advance the reliability and reasoning capability of frontier models
• Potential for ongoing work and contract extension as new projects launch