Researcher - Lean 4 & Formal Proof Systems

About The Role

What if your deepest mathematical expertise could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs — pushing the boundaries of what proof assistants can express, capture, and automate.

This is a fully remote, flexible contract role built for researchers who thrive on rigor, precision, and intellectual challenge. If you find satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify, this role was made 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 proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test 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 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 why — complexity, missing lemmas, insufficient libraries, and beyond
• 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
• Possess a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete math
• Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean 4 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal mathematical arguments into clean, structured formal proofs independently
• Naturally precise, patient, and driven by structural elegance and logical completeness

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 reasoning strategies

Why Join Us

• Work on cutting-edge AI projects alongside leading research labs and top AI teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Operate at the true frontier of formal verification and mechanized mathematics
• Contribute directly to how next-generation AI systems reason about mathematics and logic
• Potential for ongoing work and contract extension as new projects launch

Key skills/competency

• Lean 4
• Formal Proof Systems
• Mathematics
• Logic
• Theoretical Computer Science
• Formal Verification
• Proof Assistants
• Mechanized Mathematics
• AI Training
• Research