Researcher - Lean 4 & Formal Proof Systems
Researcher — Lean 4 & Formal Proof Systems (AI Training) About The Role What if your deep mathematical training could directly shape how AI reasons about formal proofs — pushing the boundaries of what machines can understand and verify? We're looking for mathematicians and formal verification experts to translate sophisticated mathematical arguments into Lean 4, working at the intersection of pure mathematics and cutting-edge AI research. This is a fully remote, flexible contract role. If you find genuine satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify — 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 a focus on clarity, structure, and correctness
- Analyze proofs across domains, identifying gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test and extend the limits of existing proof assistants — especially where tools struggle or fail
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Develop 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
- Investigate where automated provers break down and articulate precisely why — complexity, missing lemmas, insufficient libraries, and beyond
- Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
Who You Are
- Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Have a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
- Bring hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable system — Lean 4 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
- Mathematically mature and energized by working at the frontier of what formal systems can express
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 substantial manual scaffolding
- Prior experience with data annotation, data quality evaluation, or AI training workflows
- Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies clearly
Why Join Us
- Work on genuinely frontier problems — proofs that lie beyond the current capabilities of automated systems
- Fully remote and flexible — structure your work around your life, not the other way around
- Collaborate with teams working alongside the world's leading AI research labs
- Freelance autonomy with the depth and intellectual rigor of serious mathematical research
- Contribute to work that is actively shaping how AI understands and reasons about mathematics
- Potential for ongoing contract extension as new projects launch
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