Researcher

About the Role

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: 10–40 hours/week

Key Responsibilities

• Translate informal mathematical proofs into precise, machine-verifiable Lean 4 formalizations with an emphasis on clarity, correctness, and structure.
• Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures.
• Construct formalizations that stress-test the limits of existing proof assistants, especially where automated tools struggle or fail entirely.
• Investigate and articulate why automated provers break down — whether due to complexity, missing lemmas, or insufficient library coverage.
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms.
• Collaborate with AI researchers to refine strategies for improving formal verification pipelines.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
• Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments.
• Surface deeper patterns or generalizations implicit in the original mathematics through the formalization process.

Requirements & Tech Stack

• Lean 4
• Coq
• Isabelle/HOL
• Agda
• Proof Assistants
• Formal Verification

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable proof assistant — Lean 4 strongly preferred.
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics.
• Ability to translate dense, informal mathematical arguments into clean, structured formal proofs independently.
• Comfort working at the frontier — where tools don't always cooperate and creativity is required.

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 scenarios where automated reasoning frequently fails or requires significant manual scaffolding.
• Prior experience with data annotation, data quality evaluation, or AI training workflows.
• Strong written communication skills for explaining formalization decisions, edge cases, and proof strategies to interdisciplinary collaborators.