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 — especially Lean — to help push the boundaries of what machine‑verifiable mathematics can express.

This is a fully remote, flexible contract role working alongside leading AI research labs. You'll tackle proofs that automated tools can't yet handle, helping map the true frontier of formal verification.

- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: Adaptable

What You'll Do

- Translate informal mathematical proofs into Lean (and related proof systems) with a focus on clarity, structure, and machine‑verifiable correctness
- Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable sub‑structures
- Build formalizations that probe the limits of current proof assistants, especially where automation breaks down
- 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
- Advise on proof decomposition, lemma selection, and structuring techniques for formal models

Who You Are

- 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 a comparable system — Lean strongly preferred
- Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
- Ability to translate dense, informal arguments into clean, structured formal proofs
- Comfortable working independently on technically demanding, open‑ended problems

Nice to Have

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

Sample Work You Might Do

- Formalize classical proofs and compare machine‑verifiable structures against textbook arguments
- Investigate where automated provers break down — and articulate precisely why (complexity, missing lemmas, library gaps, etc.)
- Construct Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

Why Join Us

- Work on some of the most intellectually demanding problems at the intersection of mathematics and AI
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with meaningful, well‑defined 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

📌 Mathematical Formalization Specialist (Rincón de los Sauces)
🏢 Alignerr
📍 Rincón de los Sauces