About the Role
What if your deep mathematical expertise could directly shape how AI reasons, proves, and thinks? We're looking for Applied Formal Methods Researchers to translate rigorous human-written mathematics into machine-verifiable Lean 4 proofs — working at the exact frontier where formal verification meets the limits of modern AI.
This is a fully remote, flexible contract role built for mathematicians who love precision, structural beauty, and the challenge of expressing elegant arguments in a form a machine can actually 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 domain-specific and general proofs to identify gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test the limits 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 highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
- Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Formalize classical proofs and compare machine-verifiable structures against textbook arguments
- Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and beyond
- Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
Who You Are
- Holder of a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Deeply grounded in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
- Experienced with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean 4 strongly preferred
- Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate dense, informal arguments into clean, structured formal proofs with precision
- A methodical problem-solver who finds satisfaction in resolving gaps that automated tools cannot yet bridge
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 significant 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 directly on cutting-edge AI projects alongside leading research labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the intellectual depth of meaningful, frontier-level work
- Direct exposure to how advanced AI models are trained and where mathematical reasoning fits in
- Contribute to defining the boundary of what mechanized mathematics can express and verify
- Potential for ongoing work and contract extension as new projects launch