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: 10–40 hours/week What You'll Do Translate informal mathematical proofs into exact, 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 flexible — 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)
🏢 Alignerr
📍 Adelaide