Applied Formal Methods Researcher (Lean 4)

Alignerr Corp.; Wellington; Remote; NZD 83,000 - 165,000; Full time

Job summary

Alignerr is seeking Applied Formal Methods Researchers to translate advanced mathematical arguments into machine-verifiable Lean 4 formalizations — pushing the boundaries of what proof assistants can do. This is a fully remote, hourly contract role for mathematicians who love formal verification and enjoy turning rigorous human reasoning into machine-checkable form.

You will translate informal proofs, analyze gaps, stress-test proof systems, and collaborate to improve verification pipelines.

Qualifications

• Master's degree or higher in Mathematics, Logic, or related field.
• Strong background in formal reasoning and proof writing across algebra, analysis, topology, logic.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof assistant—Lean 4 strongly preferred.

Responsibilities

• Translate informal mathematical proofs into precise, machine-verifiable Lean scripts and formalizations.
• Analyze proofs across domains to identify gaps, assumptions, and formalizable sub-structures.
• Construct formalizations that stress-test existing proof assistants where automation breaks down.
• Investigate why automated provers fail—due to complexity, missing lemmas, or library limitations.
• Develop clean, readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms.
• Collaborate with researchers to design and 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.
• Uncover deeper patterns or generalizations in the original mathematics through the formalization process.

Skills

Analytical thinking

Mathematical rigor

Independent work

Education

Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or related field

Tools

Lean 4

Lean 3

Coq

Isabelle/HOL

Job description

About The Role

What if your deep mathematical training could directly shape how AI understands and reasons about formal proof? We're looking for Applied Formal Methods Researchers to translate advanced mathematical arguments into machine-verifiable Lean 4 formalizations — working at the very edge of what modern proof assistants can do. This is a fully remote, flexible contract role for mathematicians who are passionate about formal verification and excited by the challenge of expressing rigorous human reasoning in a form a machine can check, validate, and learn from.

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

What You'll Do

• Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4
• Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that stress-test existing proof assistants, especially where automation breaks down
• Investigate and articulate why automated provers fail — whether due to complexity, missing lemmas, or library limitations
• Develop clean, readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Collaborate with researchers to design and 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
• Uncover deeper patterns or generalizations implicit in the original mathematics through the formalization process

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 a comparable proof assistant — Lean 4 strongly preferred
• Find genuine satisfaction in translating dense, elegant human arguments into precise formal structures
• Appreciate the structural beauty of formal proofs and the challenge of resolving gaps that automated tools cannot yet bridge
• Are self‑motivated and comfortable working independently and asynchronously

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 requires manual scaffolding
• Prior experience with data annotation, data quality, or AI evaluation workflows
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work alongside world‑leading AI research teams on genuinely frontier problems in mechanized mathematics
• Fully remote and flexible — work when and where it suits you, at a pace that fits your schedule
• Freelance autonomy with the intellectual depth of meaningful, research‑grade work
• Contribute directly to the future of how AI understands and generates formal mathematical reasoning
• Potential for ongoing work and contract extension as new projects launch