Formal Verification Scientist (Lean 4 & Mathlib)

Alignerr Corp.; Wellington; Remote; NZD 149,000 - 298,000; Part time

Benefits offered by this job

Fully remote

Flexible schedule

Freelance autonomy

Work on frontier AI research

Job summary

Alignerr is seeking a Formal Verification Scientist to translate advanced mathematics into Lean 4 proofs for AI reasoning about truth and knowledge. This is a fully remote, hourly contract role designed for mathematicians passionate about rigorous proof, formal systems, and mechanized mathematics.

As a key collaborator with AI researchers, you will formalize proofs, analyze sub-structures, and push proof assistants beyond current capabilities while maintaining machine-verifiable precision.

Qualifications

• Master's degree or higher in Mathematics, Logic, or related field.
• Strong background in rigorous proof writing and formal systems.
• Experience with Lean, Coq, Isabelle/HOL or similar tools.
• Ability to translate informal arguments into machine-verifiable proofs.

Responsibilities

• Translate informal mathematical proofs into clean Lean 4 formalizations with clarity and correctness.
• Analyze proofs to identify hidden assumptions, gaps, and formalizable sub-structures.
• Push the boundaries of proof assistants on hard problems where automation struggles.
• Explain why automated provers fail due to complexity, lemmas, or library gaps.
• Formalize classical proofs and compare machine-verifiable structures to textbook arguments.
• Uncover deeper patterns and generalizations in original arguments.
• Collaborate with AI researchers to design and evaluate formal verification pipelines.
• Guide proof decomposition, lemma selection, and structuring strategies for formal models.

Skills

Lean 4

Coq

Isabelle/HOL

Agda

Formal verification

Mathematical rigor

Proof decomposition

Education

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

Tools

Lean 3/4

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your deep mathematical training could directly shape how AI reasons about truth, proof, and knowledge? We're looking for Formal Verification Scientists to translate advanced human mathematics into machine-verifiable Lean 4 proofs — working at the very frontier of what automated proof assistants can express and reason about.

About The Role

What if your deep mathematical training could directly shape how AI reasons about truth, proof, and knowledge? We're looking for Formal Verification Scientists to translate advanced human mathematics into machine-verifiable Lean 4 proofs — working at the very frontier of what automated proof assistants can express and reason about.

This is a fully remote, flexible contract role built for mathematicians who are passionate about rigorous proof, formal systems, and the future of mechanized mathematics. If you find satisfaction in taking a dense, elegant argument and expressing it with the precision a machine can verify, this role was made for you.

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

What You'll Do

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations — with an emphasis on clarity, correctness, and reproducibility
• Analyze proofs across domains, identifying hidden assumptions, gaps, and formalizable sub-structures
• Push the boundaries of existing proof assistants by working on problems where automated tools struggle or fail entirely
• Investigate and articulate why automated provers break down — whether due to complexity, missing lemmas, or insufficient library coverage
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Uncover deeper patterns and generalizations implicit in original mathematical arguments
• Collaborate with AI researchers to design, refine, and evaluate formal verification pipelines
• Provide guidance on proof decomposition, lemma selection, and structuring strategies for formal models

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 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into well‑structured, machine‑verifiable formal proofs
• Mathematically mature — you appreciate precision, structural beauty, and the challenge of bridging human and machine reasoning

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

Why Join Us

• Work on cutting‑edge AI projects alongside leading research labs and teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually rigorous work
• Contribute directly to how AI understands and reasons about advanced mathematics
• Gain exposure to frontier large language models and how formal reasoning shapes their training
• Potential for ongoing work and contract extension as new projects launch