Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About The Role

What if your mathematical expertise could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems to translate rigorous human-written arguments into machine-verifiable proofs — working at the very edge of what automated tools can do today.

This is a fully remote, flexible contract role built for mathematicians who find beauty in precision and satisfaction in solving problems that automated systems simply cannot handle alone.

- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: Adaptable — work on your own schedule

What You'll Do

- Translate informal mathematical proofs into Lean (and related proof assistants) with a focus on clarity, structure, and correctness
- Analyze domain-specific and general proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that push the limits of existing proof assistants, especially where tools struggle or fail
- Collaborate with AI researchers to design and refine formal verification strategies and pipelines
- Develop clean, readable, and reproducible proof scripts aligned with mathematical best practices
- Advise on proof decomposition, lemma selection, and structuring techniques for formal models
- Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond

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 formal systems — Lean strongly preferred
- Are deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Can reliably translate dense informal arguments into clean, structured, machine-verifiable formalizations
- Work independently with precision and consistency

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 in contexts where automated reasoning requires significant manual scaffolding
- Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies to collaborators

Why This Role

- Work on cutting-edge AI research projects alongside leading AI labs and researchers
- Fully remote and flexible — structure your work around your life, not the other way around
- Apply your deepest mathematical skills to problems that genuinely matter and that automated tools cannot yet solve
- Contribute to the advancement of formal verification and AI reliability at the frontier of modern mathematics
- Potential for ongoing work and contract extension as new research projects launch

📌 Mathematical Formalization Specialist (México)
🏢 Alignerr
📍 México