Researcher — Lean 4 & Formal Proof Systems (AI Training)
About The Role
What if your mathematical expertise could directly shape how AI reasons about formal proofs — pushing the boundary of what machines can understand and verify?
We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean proofs, working on problems that sit at the very frontier of what automated systems can handle today.
This is a fully remote, flexible contract role designed for researchers who love rigor, structure, and the intellectual challenge of making the implicit explicit.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: ***** hours/week
What You'll Do
Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 (and related proof systems)
Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that test and extend the limits of existing proof assistants, especially where automation struggles or fails
Investigate the breakdown points of automated provers and articulate the underlying reasons — complexity, missing lemmas, library gaps, and more
Collaborate with research teams 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 guidance on proof decomposition, lemma selection, and structuring techniques for formal models




Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
Who You Are
Holds a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
Deeply grounded in rigorous proof construction across areas such as algebra, analysis, topology, logic, or discrete mathematics
Experienced with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean strongly preferred
Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Able to translate dense, informal mathematical arguments into clean, structured, formally verified proofs
Finds satisfaction in resolving the gaps that automated tools cannot yet bridge
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 manual scaffolding
Prior experience with data annotation, data quality, or evaluation systems
Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies
Why Join Us
Work directly on cutting-edge AI research projects alongside leading research labs
Fully remote and adaptable — work when and where it suits you
Freelance autonomy with meaningful, intellectually stimulating work at the frontier of formal mathematics
Gain rare exposure to how advanced AI models are trained on formal reasoning tasks
Potential for ongoing work and contract extension as new projects launch

📌 Researcher - Lean 4 & Formal Proof Systems (Adelaide)
🏢 JobRadars - AU
📍 Adelaide