About the Role
What if your deep mathematical expertise could directly shape how AI understands and generates formal proofs — pushing the boundaries of what machines can reason about?
We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs for cutting-edge AI research. This role sits at the frontier of mathematics and computer science, tackling proofs that often lie beyond what automated systems can currently handle.
This is a fully remote, flexible contract role built for researchers who love precision, structure, and the intellectual challenge of making rigorous human reasoning legible to machines.
- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: 10–40 hours/week
What You'll Do
- Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations
- Analyze proofs across domains — algebra, analysis, topology, logic, discrete math — identifying hidden assumptions, gaps, and formalizable sub-structures
- Construct formalizations that stress-test the limits of existing proof assistants, especially where automation breaks down
- Collaborate with researchers to design and refine strategies for improving formal verification pipelines
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
- Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Investigate where automated provers fail — and articulate precisely why (complexity, missing lemmas, library gaps, etc.)
- Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
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 one or more of: 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 4 strongly preferred
- Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate dense, informal mathematical arguments into precise, structured formal proofs
- Intellectually energized by working at the frontier — where tools struggle and human insight still matters most
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
- Prior exposure to theorem provers where automated reasoning frequently requires manual scaffolding
- Background in data annotation, data quality, or evaluation systems
- Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to collaborators
Why Join Us
- Work on genuinely frontier problems — proofs that push the limits of what machines can verify
- Collaborate with teams building cutting-edge AI models at leading research labs
- Fully remote and flexible — work when and where you do your best thinking
- Freelance autonomy with meaningful, intellectually stimulating work
- Gain rare exposure to how advanced AI models are trained on formal mathematical reasoning
- Potential for ongoing work and contract extension as new projects launch