Researcher - Lean 4 & Formal Proof Systems

Alignerr Corp.; Wellington; Remote; NZD 83,000 - 152,000; Full time

Job summary

Alignerr is seeking a researcher to translate advanced mathematical arguments into Lean 4 proofs for AI training. You will work remotely, translating informal proofs into machine-verifiable formalizations and collaborating with AI researchers to improve verification pipelines.

The role emphasizes rigorous proof development, readability, and extensibility of formal models, with freelance autonomy and flexible hours.

Qualifications

• Master's degree or higher in Mathematics, Logic, or Theoretical CS.
• Strong proof-writing background across algebra, analysis, topology, logic or discrete math.
• Experience with Lean (3 or 4) or comparable systems (Coq/Isabelle/Agda).
• Ability to express dense mathematical arguments for machine verification.

Responsibilities

• Translate informal mathematical proofs into precise, machine-verifiable Lean 4 formalizations.
• Analyze proofs to identify gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that test limits of proof assistants when automation struggles.
• Collaborate with AI researchers to refine formal verification pipelines.
• Develop readable, reproducible proof scripts aligned with best practices and idioms.
• Provide guidance on proof decomposition, lemma selection, and structuring strategies.
• Investigate failure modes of automated provers and library gaps.
• Create Lean proofs revealing deeper patterns or generalizations.

Skills

Lean

Proof writing

Formal verification

Independent work

Communication skills

Education

Master's 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 how AI reasons about formal proofs — pushing the boundaries of what machines can verify, understand, and automate? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs for cutting‑edge AI research. This is rare, high‑impact work at the intersection of mathematics and computer science — and you'll be working on problems that sit beyond the current reach of automated provers.

• 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), with a focus on clarity, correctness, and structure
• Analyze generic and domain‑specific proofs to identify gaps, hidden assumptions, and formalizable sub‑structures
• Construct formalizations that test and expand the limits of existing proof assistants — especially where automated tools struggle or fail
• Collaborate with AI 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 expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models
• Investigate where and why automated provers break down — articulating failure modes around complexity, missing lemmas, or library gaps
• Create Lean proofs that surface 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 systems — Lean is strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to take a dense, human‑written mathematical argument and express it cleanly in a form a machine can verify
• Self‑directed and rigorous — you find satisfaction in resolving the gaps that automated tools cannot yet bridge

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, evaluation systems, or AI training workflows
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work on genuinely frontier problems in formal verification and AI research
• Collaborate with teams at the cutting edge of AI and mathematical reasoning
• Fully remote and async‑friendly — work on your own schedule, from anywhere
• Freelance autonomy: choose your hours, maintain your independence
• Exposure to how advanced AI models are trained and evaluated on mathematical reasoning
• Potential for ongoing work and contract extension as new projects launch