Applied Formal Methods Researcher (Lean 4)

About The Role What if your deep mathematical expertise could directly shape how AI reasons, proves, and thinks? We're looking for Applied Formal Methods Researchers to translate rigorous human-written mathematics into machine-verifiable Lean 4 proofs — working at the exact frontier where formal verification meets the limits of modern AI. This is a fully remote, flexible contract role built for mathematicians who love precision, structural beauty, and the challenge of expressing elegant arguments in a form a machine can actually verify.

• 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 domain-specific and general proofs to identify 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 where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and beyond
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

Who You Are

• Holder of a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Deeply grounded in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Experienced with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean 4 strongly preferred
• Genuinely 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
• A methodical problem-solver who finds 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 with large-scale formalization projects such as Mathlib
• Exposure to theorem provers where automated reasoning frequently fails or requires significant 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 directly on cutting-edge AI projects alongside leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the intellectual depth of meaningful, frontier-level work
• Direct exposure to how advanced AI models are trained and where mathematical reasoning fits in
• Contribute to defining the boundary of what mechanized mathematics can express and verify
• Potential for ongoing work and contract extension as new projects launch