What We're Researching We are running a paid project focused on creating and validating complex coding tasks for AI systems. The goal is to build realistic, self-contained software engineering problems that push the boundaries of automated coding agents.
Lean 4 Proof Engineer - Mathematical Formalization
Remote (Global)
$10 – $40/hr
May 25, 2026
Job description
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
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
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
Compensation by region
Pay varies by where you're based. Each region below is open to applicants in that country only.
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Available in 11 regions: pick your country on click.
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