Join the Appen team as an Independent Contractor for Project Astra . Project Astra is seeking individuals for an ongoing, ad-hoc project focused on improving real-time conversational AI.
Researcher - Lean 4 & Formal Proof Systems
Remote (Global)
$170 – $200/hr
May 25, 2026
Job description
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 mechanized mathematics.
- 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, correctness, and structural elegance
- Analyze domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
- Construct formalizations that probe the limits of existing proof assistants — especially where automation breaks down
- Collaborate with AI 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 expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
- Investigate where automated provers fail and articulate why — complexity, missing lemmas, insufficient libraries, or structural issues
- Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
Who You Are
- Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
- Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
- Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean 4 strongly preferred
- Able to translate informal mathematical arguments into clean, structured formal proofs
- Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
Nice to Have
- Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling
- Experience contributing to large-scale formalization 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 formalization 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 when and where it suits you
- Freelance autonomy with the structure of meaningful, intellectually demanding work
- Contribute directly to advancing what AI can understand, verify, and reason about in mathematics
- Potential for ongoing work and contract extension as new projects launch
Apply now
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Join the Appen team as an Independent Contractor for Project Astra . Project Astra is seeking individuals for an ongoing, ad-hoc project focused on improving real-time conversational AI.
Join the Appen team as an Independent Contractor for Project Astra . Project Astra is seeking individuals for an ongoing, ad-hoc project focused on improving real-time conversational AI.
We are looking for AI Data Specialists to support the improvement of AI-generated content in Finnish . Job Type: Freelance Location: Work from home Work Schedule: Part-time - 10+ hours per week. Flexible - work whenever you want.