About the Role
What if your deep mathematical training could directly shape how AI reasons, verifies, and understands the most complex proofs in existence? 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 be tackling problems that automated tools can't yet solve, operating at the true frontier of formal verification.
- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: Flexible — work on your own schedule
What You'll Do
- Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and machine-verifiability
- Analyze domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test and extend the limits of existing proof assistants — especially where tools struggle or fail
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Develop 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 break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and more
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 a comparable formal proof system — Lean strongly preferred
- Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
- Able to take a dense, elegant human argument and express it in a form a machine can verify
- Detail-oriented and precise — you find satisfaction in resolving the gaps that automated tools cannot bridge
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
- Exposure to theorem provers where automated reasoning frequently requires manual scaffolding
- Strong written communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work on genuinely cutting-edge AI and mathematics research alongside leading research labs
- Fully remote and flexible — structure your work around your life, not the other way around
- Freelance autonomy with the substance of meaningful, high-impact technical work
- Contribute directly to advancing the frontier of formal verification and AI reasoning capabilities
- Potential for ongoing work and contract extension as new projects launch