About The Role
What if your deep mathematical training could directly shape how AI reasons, proves, and understands the most complex ideas in human knowledge We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — helping map the frontier of what machines can verify, and building the foundation for the next generation of AI reasoning systems.
This is a fully remote, flexible contract role for mathematicians who are passionate about formal verification and want their expertise to matter beyond the page.
- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: 10–40 hours/week
What You'll Do
- Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4
- Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable substructures
- Construct formalizations that test the limits of existing proof assistants, especially where automated tools struggle or fail
- Collaborate with researchers to design and refine strategies for improving formal verification pipelines
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices
- 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 exactly why — complexity, missing lemmas, insufficient libraries, and beyond
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 proof systems — Lean strongly preferred
- Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
- Skilled at translating dense, informal arguments into clean, structured, machine-readable proofs
- A mathematically mature 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 requires manual scaffolding
- Prior experience with data annotation, quality evaluation, or AI training workflows
- Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work at the intersection of advanced mathematics and cutting-edge AI research
- Collaborate with world-leading AI research teams and labs
- Fully remote and flexible — work on your own schedule from anywhere
- Freelance autonomy with meaningful, intellectually rigorous work
- Gain direct exposure to how frontier AI models are trained and evaluated
- Potential for ongoing engagement and contract extension as projects evolve
