Mathematical Formalization Specialist (Lean / Formal Proof Systems)

Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About the Role

What if your deep mathematical training could directly shape how AI reasons, verifies, and understands formal logic? We're looking for mathematicians with hands-on experience in formal proof systems — particularly Lean — to work at the intersection of rigorous mathematics and cutting-edge AI research.

This is a fully remote, flexible contract role built for mathematically mature problem-solvers who find satisfaction in translating elegant human arguments into precise, machine-verifiable form. You'll work on proofs that push the boundaries of what automated tools can currently handle — helping map the frontier of formal verification itself.

• 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 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 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 — uncovering complexity, missing lemmas, or insufficient libraries

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 systems — Lean strongly preferred
• Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into clean, well-structured formal proofs
• Mathematically mature — you notice the gaps that others skip over and know how to resolve them

Nice to Have

• Familiarity with type theory, the Curry–Howard correspondence, and proof automation tools
• Experience with large-scale formalization projects (e.g., mathlib)
• Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Sample Work You Might Do

• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
• Identify precisely where and why automated provers fail on a given class of problems

Why Join Us

• Work on some of the most technically demanding AI research problems in existence today
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, high-impact, task-based work
• Contribute directly to advancing the reliability and reasoning capability of frontier AI systems
• Potential for ongoing work and contract extension as new projects launch