Alignerr
Researcher - Lean 4 & Formal Proof Systems
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Researcher - Lean 4 & Formal Proof Systems
Researcher – Lean 4 & Formal Proof Systems (AI Training)
About the Role
What if your mathematical expertise could directly shape how AI reasons about proofs — pushing the boundary of what machines can understand and verify? We're looking for mathematicians and formal verification specialists to translate sophisticated human-written arguments into precise, machine-checkable Lean 4 proofs for cutting-edge AI research.
This is a fully remote, flexible contract role designed for researchers who thrive on rigor, structure, and working at the frontier of mechanised mathematics.
Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: 10–40 hours/week
Responsibilities
- Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, correctness, and structural elegance
- Analyze domain-specific proofs to identify gaps, hidden assumptions, and formalisable sub-structures
- Construct formalisations probing the limits of existing proof assistants — especially where automation breaks down
- Collaborate with AI researchers, designing, refining, and evaluating strategies for improving formal verification pipelines
- Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
- Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Investigate why automated provers fail (potential reasons: complexity, missing lemmas, insufficient libraries, or structural issues)
- Create Lean proofs that surface deeper patterns or generalisations implicit in the original mathematics
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Requirements
- Degree: Master's or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Proof Writing: Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
- Formal Systems Experience: Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems (Lean 4 strongly preferred)
- Translation Skills: Ability to translate informal mathematical arguments into clean, structured formal proofs
- Enthusiasm: Deep passion for formal verification, proof assistants, and the future of mechanised mathematics
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Nice to Have:
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling
- Experience contributing to large-scale formalisation 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 explaining formalisation decisions, edge cases, and reasoning strategies
Why Join Us
- Work on cutting-edge AI research alongside leading labs and research teams
- Fully remote and flexible work schedule
- Freelance autonomy with high-value, intellectually stimulatingwork
- Directly contribute to advancing what AI can understand, verify, and reason about in mathematics
- Potential for ongoing work and contract extension as new projects launch
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