Researcher - Lean 4 & Formal Proof Systems

Alignerr Corp.; Brisbane; Remote; AUD 83,000 - 131,000; Part time

Job summary

Alignerr is seeking a Researcher to translate informal mathematical proofs into Lean 4 and related proof systems for AI training. You will express dense arguments in machine-verifiable form with emphasis on structure and correctness.

Responsibilities include analyzing proofs across domains, identifying gaps, and constructing formalizations that push proof assistants. Collaboration aims to improve verification pipelines and reproducible scripts.

Qualifications

• Master's degree or higher in Mathematics, Logic, or Theoretical CS.
• Strong proof-writing background across algebra/analysis/topology/logical domains.
• Hands-on experience with Lean, Coq, Isabelle/HOL, or Agda.

Responsibilities

• Translate informal proofs into Lean 4 proofs with clarity and correctness.
• Analyze proofs to find gaps, assumptions, and formalizable sub-structures.
• Construct formalizations that test proof assistants' limits and automation.
• Collaborate to improve verification pipelines and strategies.
• Develop readable proof scripts aligned with mathematical best practices.

Skills

Lean 4

Formal verification

Proof writing

Mathematical reasoning

Education

Master's degree in Mathematics or related field

Tools

Lean (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 arguments into machine-verifiable Lean 4 proofs — working at the precise boundary where human mathematical intuition meets the rigorous demands of proof assistants.

This is a fully remote, flexible contract role for researchers who love structure, precision, and pushing the limits of what formal systems can express. If you find satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify, this role was built for you.

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

What You'll Do

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, structure, and correctness
• Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test the limits of existing proof assistants, especially where automation breaks down
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers fail — and clearly articulate why (complexity, missing lemmas, library gaps, etc.)
• 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 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into clean, well‑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, data quality, or AI evaluation workflows
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work on cutting‑edge AI research projects alongside world‑leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, high‑impact technical work
• Contribute directly to advancing what AI can understand, reason about, and verify in mathematics
• Potential for ongoing work and contract extension as new projects launch