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 — 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: Flexible

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