Researcher - Lean 4 & Formal Proof Systems
Researcher - Lean 4 & Formal Proof Systems What if your mathematical expertise could directly shape the future of AI reasoning? We're looking for mathematicians and formal verification specialists to translate sophisticated human-written proofs into machine-verifiable Lean 4 formalizations — working at the very edge of what proof assistants can currently express and automate. This is a fully remote, flexible contract role designed for researchers who love rigor, thrive on precision, and want their work to matter at the frontier of AI and mechanized mathematics.
- 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 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 push the limits of existing proof assistants, especially where automation fails
- Investigate why automated provers break down — complexity, missing lemmas, insufficient libraries — and document your findings
- Develop clean, reproducible proof scripts aligned with mathematical best practices and Lean idioms
- Advise on proof decomposition, lemma selection, and structuring strategies for formal models
- Collaborate with researchers to design and evaluate approaches for improving formal verification pipelines
- 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
- Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean 4 strongly preferred
- Deeply passionate about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate dense, informal mathematical arguments into clean, structured, machine-verifiable proofs
- Comfortable working independently and asynchronously in a remote environment
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 in settings where automated reasoning frequently fails or requires manual scaffolding
- Prior experience with data annotation, evaluation systems, or AI training workflows
- Strong communication skills for articulating formalization decisions, edge cases, and proof strategies
Why This Role Stands Out
- Work on problems that sit at the genuine frontier of formal verification and AI research
- Collaborate with teams at leading AI research labs on cutting-edge projects
- Gain direct exposure to how advanced AI models are trained and evaluated
- Fully remote and asynchronous — work on your own schedule, from anywhere
- Freelance autonomy with meaningful, intellectually rich work
- Potential for ongoing contract extension as new projects launch
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