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