Researcher - Lean 4 & Formal Proof Systems

Researcher — Lean 4 & Formal Proof Systems (AI Training)About The Role What if your deep mathematical expertise could directly shape how AI reasons, verifies, and understands formal proofs? We're looking for mathematicians and formal verification specialists to translate sophisticated mathematical arguments into machine-verifiable Lean 4 proofs — working at the very edge of what modern proof assistants can do. This is a fully remote, flexible contract role built for researchers who love rigor, structure, and the challenge of pushing formal systems to their limits.

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: 10–40 hours/week

What You'll Do

• Translate informal, human-written mathematical proofs into precise, machine-verifiable Lean 4 formalizations
• Analyze proofs across domains — algebra, analysis, topology, logic, discrete math — identifying hidden assumptions, gaps, and formalizable sub-structures
• Construct formalizations that probe the boundaries of existing proof assistants, especially where automated tools struggle or fail
• Develop clean, readable, and reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Collaborate with researchers to design, refine, and evaluate strategies for advancing formal verification pipelines
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, library gaps, and more
• 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
• Have a strong foundation in rigorous proof writing and mathematical reasoning across one or more 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 dense, informal arguments into clean, structured formal proofs with precision and clarity
• Self-motivated and comfortable working independently in an asynchronous, remote environment

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 articulating formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work on cutting-edge AI projects alongside leading research labs
• 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 what AI can understand, verify, and reason about in mathematics
• Potential for ongoing work and contract extension as new projects launch