About the Role
What if your deep mathematical training could directly shape the future of AI — and help machines understand the most rigorous arguments the human mind can produce?
We're looking for expert mathematicians with hands-on experience in formal proof systems to translate advanced mathematical reasoning into machine-verifiable Lean 4 code. This role sits at the frontier of what proof assistants can express, capture, and automate — and you'll be the one mapping that frontier.
This is a fully remote, flexible contract role for mathematicians who care deeply about precision, structure, and the art of formal argumentation.
- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: 10–40 hours/week
What You'll Do
- Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on correctness and clarity
- Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures
- Construct formalizations that test and expose the limits of existing proof assistants
- Collaborate with AI researchers to design and evaluate strategies for improving formal verification pipelines
- Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
- Guide proof decomposition, lemma selection, and structuring techniques for formal models
- Investigate where automated provers break down — and articulate precisely why
- Create Lean proofs that reveal 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
- Possess 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 systems — Lean 4 strongly preferred
- Thrive at the intersection of mathematics and formal computer science
- Take satisfaction in translating dense, elegant human arguments into forms a machine can fully verify
- Appreciate precision, structural beauty, and the challenge of resolving gaps that automated tools cannot yet bridge
Nice to Have
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
- Experience contributing to large-scale formalization projects (e.g., Mathlib)
- Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
- Prior experience with data annotation, quality evaluation, or AI training workflows
- Strong communication skills for articulating formalization decisions, edge cases, and proof strategies
Why Join Us
- Work directly on cutting-edge AI research alongside leading labs and researchers
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually rigorous work
- Operate at the frontier of mechanized mathematics — pushing what formal verification can achieve
- Potential for ongoing work and contract extension as new projects launch