About the Role
What if your deep mathematical training could directly shape how AI reasons about formal proofs — and help push the boundaries of what machines can understand and verify?
We're looking for mathematicians with serious proof-writing chops and hands-on experience with formal proof systems to work on one of the most intellectually demanding challenges in AI today: translating complex human mathematical arguments into machine-verifiable formalizations using Lean 4.
This is a fully remote, flexible contract role. If you live at the intersection of rigorous mathematics and formal verification — and you find satisfaction in the precision of making a dense, elegant argument machine-checkable — this role was built for you.
- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: 10–40 hours/week
What You'll Do
- Translate informal mathematical proofs into Lean 4 (and related proof systems) with emphasis on clarity, structure, and correctness
- Analyze domain-specific and general proofs, identifying hidden assumptions, logical gaps, and formalizable sub-structures
- Construct formalizations that test and extend the capabilities of existing proof assistants — especially where automated tools struggle or fail
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Develop readable, reproducible proof scripts that align 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 root causes — complexity, missing lemmas, library gaps, and beyond
- Uncover deeper patterns or generalizations implicit in the original mathematics through formal expression
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 formal systems — Lean strongly preferred
- Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate informal mathematical arguments into clean, well-structured formal proofs with precision and care
Nice to Have
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling
- Experience contributing to large-scale formalization projects such as Mathlib
- Exposure to theorem provers in settings where automated reasoning frequently fails or requires significant manual scaffolding
- Prior experience with data annotation, data quality evaluation, or AI training workflows
- Strong written communication skills for explaining formalization decisions, edge cases, and reasoning strategies to collaborators
Why Join Us
- Work at the absolute frontier of formal mathematics and AI research
- Collaborate with world-leading AI research teams and labs on genuinely hard problems
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with meaningful, intellectually stimulating work
- Contribute to shaping how AI systems understand, generate, and verify mathematical reasoning
- Potential for ongoing work and contract extension as new projects launch