About The Role What if your deep mathematical training could directly shape how AI reasons, proves, and understands the structures underlying all of mathematics? We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — pushing the boundaries of what automated reasoning can express, verify, and learn from. This is a fully remote, flexible contract role built for mathematicians who live at the intersection of rigorous proof construction and cutting-edge AI research.

If you find satisfaction in translating a dense, elegant human argument into something a machine can verify step by step, this role was made for you.

Organization: Alignerr

Type: Hourly Contract

Location: Remote

Commitment: 10–40 hours/week What You'll Do Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4 (and related proof systems)

Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures

Construct formalizations that probe and expose the limits of existing proof assistants, especially where automation breaks down

Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines

Develop clean, readable, reproducible proof scripts that align with mathematical best practices and proof assistant idioms

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

Investigate precisely where and why automated provers fail — complexity, missing lemmas, library gaps — and document your findings clearly





Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics Who You Are Graduate-level mathematician (Master's 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 formal proof systems — Lean strongly preferred

Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics

Able to translate informal arguments into clean, structured formal proofs with precision and clarity A methodical problem-solver who appreciates structural beauty and thrives working at the frontier 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 evaluation, or AI training workflows

Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to a research audience Why Join Us Work on cutting-edge AI projects alongside leading research labs and AI teams

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

Freelance autonomy with the structure of meaningful, intellectually demanding work

Contribute directly to research that is defining how AI understands and reasons about mathematics

Potential for ongoing work and contract extension as new projects launch

📌 Applied Formal Methods Researcher (Lean 4) (Perth)
🏢 Alignerr
📍 Perth