About the Role
What if your deep mathematical expertise could directly shape how AI reasons about formal proofs — pushing the boundary of what machines can understand and verify? We're looking for mathematicians and formal verification specialists to translate sophisticated human-written proofs into Lean 4, working at the cutting edge of mechanized mathematics and AI research.
This is a fully remote, flexible contract role for researchers who love rigor, thrive on precision, and find genuine satisfaction in expressing elegant mathematical arguments in a form a machine can verify.
- 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 an emphasis on clarity, structure, and correctness
- Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test the limits of existing proof assistants, especially where automation struggles or fails
- Investigate and articulate where automated provers break down — due to complexity, missing lemmas, insufficient libraries, or other factors
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Formalize classical proofs and compare machine-verifiable structures against textbook arguments
- Surface deeper patterns or generalizations implicit in the original mathematics
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 and mathematical reasoning — across algebra, analysis, topology, logic, or discrete mathematics
- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean strongly preferred
- Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate informal arguments into clean, structured, machine-verifiable formal proofs
- Mathematically mature and comfortable working at the frontier of what proof assistants can currently express
Nice to Have
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
- Experience with large-scale formalization projects such as mathlib
- Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
- Prior experience with data annotation, data quality, or evaluation systems
- Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work on cutting-edge AI projects alongside leading research labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually stimulating work
- Contribute directly to advancing the capabilities of AI in formal reasoning and mathematics
- Potential for ongoing work and contract extension as new projects launch