Researcher - Lean 4 & Formal Proof Systems

About The Role

What if your expertise in rigorous mathematical proof could directly shape the future of AI reasoning? We're looking for mathematicians and formal verification specialists to translate sophisticated human-written proofs into machine-verifiable Lean 4 formalizations --- working at the very edge of what proof assistants can express and automate.

This is a fully remote, flexible contract role designed for researchers who love precision, structural elegance, and the challenge of pushing formal verification to its limits.

• 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 a focus on clarity, structure, and correctness
• Analyze domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants --- especially where automated tools struggle or fail
• 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
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate where automated provers break down and articulate precisely why --- complexity, missing lemmas, insufficient libraries, and beyond
• Create Lean proofs that surface 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
• Possess 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
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal mathematical arguments into clean, structured formal proofs
• A mathematically mature problem-solver who finds genuine satisfaction in resolving gaps that automated tools cannot yet bridge

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 manual scaffolding
• Prior experience with data annotation, data quality, or evaluation systems
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work on cutting-edge AI research projects alongside leading research labs and AI teams
• Fully remote and flexible --- work when and where it suits you
• Freelance autonomy with meaningful, intellectually stimulating work
• Contribute directly to advancing the frontier of formal verification and AI mathematical reasoning
• Exposure to how advanced LLMs are trained and evaluated on mathematical tasks
• Potential for ongoing work and contract extension as new projects launch