About the Role
What if your deep mathematical expertise could directly influence how the world's most advanced AI systems reason, prove, and think? We're looking for Lean 4 Proof Engineers to translate rigorous human mathematics into machine-verifiable formalizations — working at the precise frontier where formal verification meets cutting-edge AI research.
This is a fully remote, flexible contract role built for mathematicians who find beauty in precision and satisfaction in expressing dense, elegant arguments in a form a machine can verify and learn from.
- Organization: Alignerr
- Type: Hourly Contract
- Location: Remote
- Commitment: 10–40 hours/week
What You'll Do
- Translate informal mathematical proofs into Lean 4 — emphasizing clarity, correctness, and structural elegance
- Analyze proofs across domains, identifying hidden assumptions, logical gaps, and formalizable substructures
- Construct formalizations that push proof assistants to their limits — especially where automated tools struggle or fail entirely
- Collaborate with AI researchers to design and refine formal verification strategies and pipelines
- Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
- Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Formalize classical and advanced proofs, then compare machine-verifiable structures against textbook arguments
- Articulate precisely where and why automated provers break down — and help map a path forward
Who You Are
- Advanced degree (Master's or PhD) in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Strong foundation in rigorous proof construction across areas such as algebra, analysis, topology, logic, or discrete mathematics
- Hands-on experience with Lean (Lean 3 or Lean 4) — Lean 4 strongly preferred
- Experience with formal proof systems such as Coq, Isabelle/HOL, or Agda is a strong plus
- Deeply enthusiastic about formal verification, proof assistants, and mechanized mathematics
- Able to translate informal arguments into clean, structured, machine-verifiable proofs
- Self-directed and comfortable working independently on complex, open-ended problems
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 fails or requires manual scaffolding
- Prior experience with data annotation, data quality, or AI evaluation systems
- Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work on genuinely frontier problems — proofs that exceed the current capabilities of automated systems
- Collaborate with leading AI research labs on cutting-edge model training
- Gain direct exposure to how advanced LLMs are trained to reason mathematically
- Fully remote and asynchronous — work when and where it suits you
- Freelance autonomy with meaningful, intellectually stimulating work
- Potential for ongoing contract extension as new research projects launch