Lean 4 Proof Engineer - Mathematical Formalization

Alignerr Corp.; Auckland; Remote; NZD 83,000 - 165,000; Part time

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to formalize advanced mathematical arguments for AI reasoning. You will translate informal proofs into machine-checkable Lean 4 formalizations with precision, structure, and rigor.

This fully remote hourly contract offers 10–40 hours per week for mathematicians who love formal verification, problem solving, and collaborating with AI researchers to push the limits of proof automation.

Qualifications

• Master's degree or higher in Mathematics, Logic, or theoretical CS.
• Strong proof-writing and formalization experience.
• Experience with Lean 3 or Lean 4, Coq, Isabelle/HOL, or similar.

Responsibilities

• Translate informal proofs into Lean 4 formalizations with clarity and correctness.
• Identify gaps and formalizable sub-structures in proofs.
• Develop readable, reproducible proof scripts aligned with best practices.
• Collaborate with AI researchers to improve verification pipelines.
• Formalize classical proofs and compare machine vs textbook arguments.
• Investigate automation limitations of provers and libraries.

Skills

Proof writing

Lean 4

Mathematics

Formal verification

Collaboration

Communication

Education

Master's degree in Math

PhD preferred

Tools

Lean

Coq

Isabelle/HOL

Agda

Mathlib

Job description

Lean 4 Proof Engineer — Mathematical Formalization

About The Role

What if your deepest mathematical instincts could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians with serious proof-writing chops to formalize advanced mathematical arguments in Lean 4 — working at the very frontier of what modern proof assistants can express, verify, and automate.

This is a fully remote, flexible contract role built for mathematicians who love precision, structure, and the challenge of translating elegant human reasoning into machine-verifiable form.

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

What You'll Do

• Translate informal mathematical proofs into rigorous, machine-verifiable Lean 4 formalizations with an emphasis on clarity, correctness, and structure
• Identify gaps, hidden assumptions, and formalizable sub-structures within generic and domain-specific proofs
• Construct formalizations that probe the limits of existing proof assistants — especially where automated tools struggle or fail entirely
• 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 techniques for formal models
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate and articulate the breakdown points of automated provers — complexity barriers, missing lemmas, insufficient libraries, and more
• Surface deeper patterns or generalizations implicit in the original mathematics through Lean proof construction

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 is strongly preferred
• Genuinely excited about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal mathematical arguments into clean, structured formal proofs with precision and care

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 significant manual scaffolding
• Prior experience with data annotation, evaluation systems, or AI training workflows
• Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies to non-specialist collaborators

Why Join Us

• Work on cutting-edge AI projects alongside leading research labs and AI teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Get direct exposure to advanced LLMs and how they are trained on formal mathematical reasoningContribute to work that is actively pushing the boundary of what AI can understand and verify
• Potential for ongoing work and contract extension as new projects launch