Researcher - Lean 4 & Formal Proof Systems

Alignerr Corp.; Auckland; Remote; NZD 83,000 - 152,000; Part time

Job summary

Alignerr is seeking researchers to translate informal mathematics into Lean 4 and related proof systems. You will analyze, formalize, and extend proofs, probing the limits of proof assistants while collaborating with peers to improve verification pipelines.

The role emphasizes deep mathematical training, a passion for formal verification, and the ability to express complex reasoning in machine-verifiable form. This is a fully remote hourly contract, offering flexible hours.

Qualifications

• Hold a 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 comparable formal systems - Lean strongly preferred.

Responsibilities

• Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 (and related proof systems).
• Analyze proofs across domains - identifying gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that probe the limits of existing proof assistants, especially where automation breaks down.
• Collaborate with researchers to design and refine strategies for improving formal verification pipelines.
• Develop clean, readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques.
• Investigate where automated provers fail - and articulate precisely why (complexity, missing lemmas, library gaps, etc.).
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics.

Skills

Proof writing

Formal verification

Abstract reasoning

Collaboration

Education

Master's degree or higher in Mathematics/Logic/Theoretical CS

Tools

Lean 3/4

Coq

Isabelle/HOL

Agda

Job description

Researcher – Lean 4 & Formal Proof Systems (AI Training)

About The Role

What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical proofs into Lean 4 - working at the frontier of what machines can understand, verify, and learn from.

This is a fully remote, flexible contract role for researchers who love rigor, find beauty in structure, and are energized by problems that push automated tools to their limits.

• 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 (and related proof systems)
• Analyze proofs across domains - identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that probe the limits of existing proof assistants, especially where automation breaks down
• Collaborate with researchers to design and refine strategies for improving formal verification pipelines
• Develop clean, readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
• Investigate where automated provers fail - and articulate precisely why (complexity, missing lemmas, library gaps, etc.)
• 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
• Possess 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 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate complex informal arguments into clean, well‑structured formal proofs
• A mathematically mature problem‑solver who finds satisfaction in expressing elegant human reasoning in a form a machine can verify

Nice to Have

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
• Experience with 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 evaluation systems
• Strong communication skills for explaining formalization decisions and reasoning strategies

Why Join Us

• Work on cutting‑edge AI projects alongside leading research labs
• Fully remote and flexible - work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Contribute directly to advancing the capabilities of AI reasoning and formal verification
• Potential for ongoing work and contract extension as new projects launch