Lean 4 Proof Engineer - Mathematical Formalization

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

Benefits offered by this job

Fully remote

Freelance autonomy

Collaborate with AI teams

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to translate advanced mathematical arguments into machine-verifiable formalizations, pushing the frontier of proof assistants and automated verification. This remote, hourly contract invites mathematicians who thrive on rigorous proof construction to contribute to AI research at the cutting edge.

You will translate informal arguments into precise Lean proofs, analyze gaps, and collaborate with AI researchers to refine verification pipelines.

Qualifications

• Master's degree or higher in Mathematics, Logic, or theoretical computer science.
• Strong proof-writing and formalization experience.
• Experience with Lean (Lean 3/4) or other proof assistants is highly desired.
• Ability to work independently on rigorous formalization tasks.

Responsibilities

• Translate informal proofs into Lean 4 formalizations with clarity and correctness.
• Analyze proofs to identify gaps and formalizable sub-structures.
• Push the boundaries of proof assistants by constructing challenging formalizations.
• Collaborate with AI researchers to improve verification pipelines.
• Develop clean proof scripts in Lean idioms and maintain reproducibility.
• Explain formalization decisions and edge cases clearly.
• Investigate automated provers' weaknesses and document findings.

Skills

Advanced mathematics

Formal proof writing

Independent work

Strong analytical thinking

Education

Master's degree or higher in Mathematics, Logic, or TCS

Tools

Lean (Lean 3/4)

Coq

Isabelle/HOL

Agda

Job description

Lean 4 Proof Engineer — Mathematical Formalization

What if your deep mathematical expertise could directly shape how AI understands and reasons about formal proof? We're looking for Lean 4 Proof Engineers to translate advanced mathematical arguments into machine-verifiable formalizations — working at the very frontier of what proof assistants can express and automate.

This is a fully remote, flexible contract role designed for mathematicians who live and breathe rigorous proof construction and want to apply that expertise to one of the most technically demanding challenges in AI research today.

About The Role

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

What You'll Do

• Translate informal mathematical proofs into precise, machine-verifiable Lean 4 formalizations with an emphasis on clarity, structure, and correctness
• Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Push the limits of existing proof assistants by constructing formalizations where automated tools struggle or fail
• Collaborate with AI researchers to design and refine strategies for improving formal verification pipelines
• Develop clean, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
• Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and more
• Formalize classical proofs and compare machine-verifiable structures against established textbook arguments

Who You Are

• 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 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, structured formal proofs independently

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

Why Join Us

• Work on genuinely frontier problems at the intersection of mathematics and AI — this is not routine annotation work
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, technically rigorous work
• Collaborate directly with world-leading AI research teams and labs
• Exposure to how advanced large language models are trained on formal mathematical reasoning
• Potential for ongoing work and contract extension as new projects launch