Researcher - Lean 4 & Formal Proof Systems

Researcher – Lean 4 & Formal Proof Systems (AI Training)

About the Role

What if your deep mathematical training could directly shape how AI understands and reasons about formal proofs — advancing the frontier of mechanized mathematics for millions of future users?

We're looking for mathematicians and formal verification specialists to write and formalize advanced mathematical proofs in Lean 4 for cutting-edge AI research. This role sits at the intersection of mathematics and computer science, translating rigorous human arguments into precise, machine-verifiable formalizations that push the limits of what proof assistants can express and automate.

This is a fully remote, flexible contract role designed for researchers who love structure, precision, and working at the edge of what's formally possible.

• 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 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 guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate and articulate where automated provers break down — due to complexity, missing lemmas, insufficient libraries, or other factors
• 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 comparable systems — Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into clean, structured formal proofs with precision and care
• A mathematically mature problem-solver who finds satisfaction in expressing dense, elegant human arguments in a form a machine can verify

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, 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 projects alongside leading research labs and teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, high-impact technical work
• Contribute directly to advancing the capabilities of AI at the frontier of formal mathematics
• Potential for ongoing work and contract extension as new projects launch
• Collaborate with a global community of researchers tackling some of the hardest problems in formal verification