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 boundaries of what machines can verify, understand, and automate? We're looking for mathematicians and formal verification researchers to translate sophisticated mathematical arguments into rigorous, machine-verifiable Lean 4 proofs.

This is frontier work: you'll be operating at the edge of what proof assistants can currently do, helping map the limits of mechanized mathematics and contributing to cutting-edge AI research. This is a fully remote, flexible contract role designed for researchers who thrive on precision, structure, and intellectual challenge.

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 gaps, hidden assumptions, and formalizable sub-structures

Construct formalizations that probe the limits of existing proof assistants, especially in areas 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 Lean idioms

Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models

Investigate where automated provers fail — and articulate precisely why (complexity, missing lemmas, library gaps, etc.)





Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics Who You Are Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field

Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics

Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof systems — Lean 4 strongly preferred

Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics

Ability to translate dense, informal arguments into precise, structured formal proofs

Mathematically mature and comfortable working at the frontier — where tools struggle and human insight is essential 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 in contexts where automated reasoning frequently requires manual scaffolding

Prior experience with data annotation, quality evaluation, or AI training workflows

Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies Why Join Us Work on some of the most intellectually demanding problems in AI and formal mathematics

Fully remote and adaptable — work when and where it suits you

Freelance autonomy with meaningful, high-impact research tasks

Collaborate with researchers at the forefront of AI development

Gain direct exposure to how advanced AI models are trained and evaluated

Potential for ongoing work and contract extension as new projects launch

📌 Researcher - Lean 4 & Formal Proof Systems (Sydney)
🏢 Alignerr
📍 Sydney