Alignerr
Applied Formal Methods Researcher (Lean 4)
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Applied Formal Methods Researcher (Lean 4)
Applied Formal Methods Researcher (Lean 4) – Formal Proof Automation (Contract)
About the Role
What if your deep mathematical training could directly shape how AI reasons, proves, and understands mathematics at a fundamental level?
We’re looking for Applied Formal Methods Researchers to formalize advanced mathematical proofs in Lean 4 — working at the precise intersection of rigorous mathematics and cutting-edge AI research.
This is a fully remote, flexible contract role designed for mathematicians who are passionate about formal verification and want their expertise to matter at scale.
Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: 10–40 hours/week
What You’ll Do
- Translate informal mathematical proofs into clean, machine-verifiable Lean 4 formalizations, with emphasis on clarity, structure, and correctness
- Analyze both generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that probe the limits of existing proof assistants, particularly where automation fails or falls short
- Collaborate with 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 for formal models
- Investigate where automated provers break down — articulating underlying challenges (complexity, missing lemmas, insufficient libraries, etc.)
- Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
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Who You Are
Must-Have Requirements
-
Hold a Master’s degree or higher in:
- Mathematics
- Logic
- Theoretical Computer Science
- Or a closely related field
-
Possess a strong foundation in rigorous proof writing across areas including (but not limited to):
- Algebra
- Analysis
- Topology
- Logic
- Discrete mathematics
-
Have hands-on experience with:
- Lean (Lean 3 or Lean 4) (Lean strongly preferred)
- Coq, Isabelle/HOL, Agda (or comparable proof systems)
-
Deeply enthusiastic about:
- Formal verification
- Proof assistants
- The future of mechanised mathematics
-
Able to translate informal mathematical arguments into clean, structured, precise formal proofs
-
Thrive working:
- Independently
- Asynchronously
- At the frontier of a fast-moving, inter-disciplinary field
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Nice-to-Have Qualities
- Familiarity with:
- Type theory
- The Curry-Howard correspondence
- Proof automation tools
- Experience contributing to:
- Large-scale formalisation projects (e.g., Mathlib)
- Exposure to theorem provers where automated reasoning fails or requires manual scaffolding
- Prior experience with:
- Data annotation
- Data quality evaluation
- AI training workflows
- Strong communication skills for:
- Articulating formalisation decisions
- Explaining edge cases
- Clarifying proof reasoning strategies
Why Join Us?
- Work directly with world-leading AI research teams on projects at the cutting edge of formal mathematics and AI
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with meaningful, intellectually stimulating work
- Gain rare exposure to how advanced AI models are trained to reason mathematically
- Contribute to defining the frontier of:
- What formal verification can express
- What it can capture
- What it can automate
- Potential for ongoing work and contract extension as new projects launch
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