About The Role What if your deep mathematical training could directly shape how AI understands and constructs formal proofs? We're looking for mathematicians with hands-on experience in formal verification to work at one of the most exciting intersections in modern AI research — mechanized mathematics. You'll translate rigorous human-written arguments into machine-verifiable Lean 4 proofs, explore the boundaries of what automated provers can and cannot do, and help build the datasets that train the next generation of AI reasoning systems.

This is a fully remote, flexible contract role designed for mathematicians who love precision, structure, and the intellectual challenge of formal verification.

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 correctness and readability

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

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

Investigate why automated provers fail on specific problems — whether due to complexity, missing lemmas, or insufficient libraries — and document your findings clearly

Collaborate with AI researchers to refine strategies for improving formal verification pipelines

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

Develop highly reproducible proof scripts aligned with mathematical best practices and Lean idioms

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





Robust 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), with Lean 4 strongly preferred — experience with Coq, Isabelle/HOL, or Agda also considered

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

Able to translate dense, informal mathematical arguments into precise, machine-checkable formal proofs

Self-directed and comfortable working independently in an asynchronous, remote environment 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 requires manual scaffolding

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

Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies The Ideal Candidate You're a mathematically mature problem-solver who thrives at the frontier of formal verification. You find genuine satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify. You appreciate precision and structural beauty — and you're energized by the challenge of resolving gaps that automated tools cannot yet bridge.

Why Join Us Work directly on cutting-edge AI research projects alongside leading AI labs

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

Freelance autonomy: set your own pace within a 10–40 hour weekly range

Gain rare exposure to how advanced AI reasoning systems are built and trained

Contribute to research that is actively pushing the frontier of what machines can prove

Potential for ongoing work and contract extension as new projects launch

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