Researcher - Lean 4 & Formal Proof Systems
Alignerr · Chicago, IL · Today
RemoteRemoteAnalystContract
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
- Create 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
- Be 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
- Be 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