Applied Formal Methods Researcher (Lean 4)

About the Role

Alignerr is seeking Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4. This is a fully remote, flexible contract role for mathematicians passionate about formal verification and pushing the limits of proof assistants.

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

Key Responsibilities

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, structure, and correctness.
• Analyze domain-specific and general proofs, identifying gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that test the limits of existing proof assistants, especially where automated tools struggle or fail.
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
• Develop highly 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 why (complexity, missing lemmas, insufficient libraries, or otherwise).
• Reveal deeper patterns and generalizations implicit in the original mathematics through formalizations.

Requirements & Tech Stack

• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof systems — Lean 4 strongly preferred.
• Able to translate informal mathematical arguments into clean, structured formal proofs.
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics.
• A mathematically mature problem-solver who finds satisfaction in expressing elegant human arguments in a form a machine can verify.

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete mathematics.

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.