Applied Formal Methods Researcher (Lean 4)

Applied Formal Methods Researcher (Lean 4)

About the Role

What if your deep mathematical expertise could directly shape how the world's most advanced AI systems reason, verify, and understand formal logic? We're looking for Applied Formal Methods Researchers to translate complex mathematical arguments into machine-verifiable Lean 4 proofs — working at the very frontier of what proof assistants can express and automate.

This is a fully remote, flexible contract role for mathematicians who find beauty in precision and satisfaction in conquering problems that automated tools simply cannot yet solve.

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

What You'll Do

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility
• Analyze both general and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants, especially where tools struggle or fail entirely
• Investigate where automated provers break down and clearly articulate why — whether due to complexity, missing lemmas, or insufficient libraries
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments to reveal deeper patterns or generalizations

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 and mathematical reasoning — across algebra, analysis, topology, logic, discrete mathematics, or related areas
• Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal proof systems — Lean 4 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to bridge the gap between informal human arguments and precise, machine-verifiable formalizations
• Thrive 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 in settings where automated reasoning frequently requires manual scaffolding
• Prior experience with data annotation, evaluation systems, or data quality workflows
• Strong communication skills for articulating formalization decisions, edge cases, and proof strategies to collaborators

Why Join Us

• Work on cutting-edge AI research projects alongside leading labs and research teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually demanding work
• Operate at the frontier of formal mathematics and AI — pushing the limits of what machines can verify
• Exposure to advanced large language models and how they are trained on formal reasoning data
• Potential for ongoing work and contract extension as new projects launch