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Researcher - Lean 4 & Formal Proof Systems
Remote (Global)
$170 – $200/hr
July 14, 2026
Job description
Researcher – Lean 4 & Formal Proof Systems
About the Role
What if your deep mathematical training could directly shape how the world's most advanced AI systems reason about proof? We're looking for mathematicians with serious formal verification chops to help us map the frontier of what machines can understand, verify, and learn from — working on proofs that push the limits of modern proof assistants like Lean 4.
This is a fully remote, flexible contract role built for mathematicians who live at the intersection of rigorous proof and formal systems. If you find genuine satisfaction in translating a dense, elegant argument into something a machine can verify — and in resolving the gaps that automated tools cannot yet bridge — this role was designed for you.
- 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 an emphasis on clarity, structure, and correctness
- Analyze generic and domain-specific proofs, identifying gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that test the limits of existing proof assistants — especially where tools struggle or fail entirely
- Collaborate with AI 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
- Formalize classical proofs and compare machine-verifiable structures against textbook arguments
- Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and more
- Create Lean proofs that reveal 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 a comparable formal proof system — Lean 4 strongly preferred
- Are genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
- Can translate informal mathematical arguments into clean, structured, machine-verifiable proofs
- Enjoy working at the frontier — where the tools haven't caught up yet and human judgment still matters
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 fails or requires extensive manual scaffolding
- Prior experience with data annotation, evaluation systems, or AI training data quality
- Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies
Why Join Us
- Work directly with teams building cutting-edge AI at leading research labs
- Fully remote and flexible — work when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually demanding work
- Contribute to a research frontier that will define how AI reasons about mathematics for years to come
- Potential for ongoing work and 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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