Alignerr
Lean 4 Proof Engineer - Mathematical Formalization
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Lean 4 Proof Engineer — Mathematical Formalization
About The Role
What if your deep mathematical training could directly shape the future of AI — and push the boundaries of what machines can reason about?
We're looking for mathematicians with formal verification expertise to translate rigorous human-written proofs into machine-verifiable Lean 4 formalizations. This role sits at the frontier of mathematics and computer science, working on problems that often lie beyond the reach of automated provers. You'll help map — and expand — what formal verification can express, capture, and automate.
This is a fully remote, flexible contract role designed for mathematically mature problem-solvers who find beauty in precision and satisfaction in resolving what automated tools cannot yet bridge.
- 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 clarity, structure, and correctness
- Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test the limits of existing proof assistants — especially where current tools struggle or fail
- Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
- Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
- Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Investigate where automated provers break down and articulate precisely why — complexity, missing lemmas, insufficient libraries, and beyond
- Formalize classical proofs and compare machine-verifiable structures against textbook arguments
- Uncover deeper patterns or generalizations implicit in the original mathematics
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Who You Are
- Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Have a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
- Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean 4 strongly preferred
- Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
- Able to translate informal arguments into clean, structured, machine-verifiable proofs
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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, evaluation systems, or AI training workflows
- Strong communication skills for explaining formalization decisions, edge cases, and proof strategies
Why Join Us
- Work on genuinely frontier problems at the intersection of mathematics and AI
- Collaborate with leading AI research teams pushing the state of the art in formal reasoning
- Fully remote and flexible — structure your work around your life
- Freelance autonomy with access to some of the most intellectually demanding problems in the field
- Exposure to advanced LLMs and how formal mathematics is used to train and evaluate them
- Potential for contract extension as new projects launch
“It took my CV and asked me questions relevant to understanding what kind of jobs to suggest for me. Suggestions were almost perfect. Jobs were exactly what I’ve been looking for.”
Jessica, London
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