About The Role What if your deep mathematical expertise could directly shape how AI reasons, proves, and understands the world's hardest problems? We're looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — working at the frontier of mechanized mathematics and cutting-edge AI research. This is a fully remote, flexible contract role built for mathematicians who thrive on precision, structural elegance, and the challenge of expressing rigorous human reasoning in a form a machine can verify.

Organization: Alignerr

Type: Hourly Contract

Location: Remote

Commitment: 10–40 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 domain-specific and general proofs to identify gaps, hidden assumptions, and formalizable sub-structures

Construct formalizations that test the limits of existing proof assistants — especially where automated tools struggle or fail

Collaborate with AI researchers 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 expert guidance on proof decomposition, lemma selection, and structuring techniques

Investigate where automated provers break down and articulate precisely why — complexity, missing lemmas, insufficient libraries, and beyond





Create Lean proofs that reveal 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

Robust foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete math

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

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

Ability to translate informal arguments into clean, structured, machine-verifiable formal proofs A mathematically mature problem-solver who finds satisfaction in resolving gaps that automated tools cannot yet bridge Nice to Have Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools

Experience with 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 explaining formalization decisions, edge cases, and reasoning strategies Why Join Us Work directly with leading AI research labs on some of the most intellectually demanding problems in formal mathematics

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

Freelance autonomy with the structure of meaningful, high-impact technical work

Contribute to defining the frontier of what AI can reason about and formally verify

Potential for ongoing work and contract extension as new projects launch

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