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: ***** 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 versatile — 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
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📌 Researcher - Lean 4 & Formal Proof Systems (Gold Coast)
🏢 Alignerr
📍 Gold Coast