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About The Role What if your deep mathematical expertise could directly shape how AI reasons, proves, and understands the most rigorous structures in mathematics? We're looking for Applied Formal Methods Researchers to translate advanced mathematical arguments into precise, machine-verifiable Lean 4 proofs — working at the very edge of what automated reasoning can do today. This is a fully remote, flexible contract role built for mathematicians who are serious about formal verification and excited by the challenge of mapping territory that automated tools can't yet navigate alone. Organization: Alignerr Type: Hourly Contract Location: Remote Commitment: 10–40 hours/week What You'll Do Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable sub-structures Construct formalizations that stress-test the limits of existing proof assistants, especially where automation breaks down Collaborate with AI researchers to design, refine, and evaluate formal verification pipelines Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms Provide expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models Investigate where automated provers fail — and articulate precisely why (complexity, missing lemmas, library gaps, etc.) Formalize classical and advanced proofs, surfacing deeper patterns and generalizations implicit in the original mathematics Who You Are Holds a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field Strong foundation in rigorous proof construction across areas such as algebra, analysis, topology, logic, or discrete mathematics Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean 4 strongly preferred Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics Able to take a dense, informal mathematical argument and express it with precision a machine can verify Naturally detail-oriented with a high tolerance for structural complexity and edge cases Nice to Have Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling Experience contributing to large-scale formalization projects such as Mathlib Exposure to theorem provers where automated reasoning frequently requires manual scaffolding Prior experience in data annotation, data quality evaluation, or AI training pipelines Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies to interdisciplinary teams Why Join Us Work on cutting-edge AI projects alongside leading research labs and frontier AI teams Fully remote and flexible — work when and where it suits you Freelance autonomy with the structure of meaningful, intellectually demanding work Direct impact on how AI learns to reason about mathematics at the highest level Potential for ongoing work and contract extension as new projects launch Join a global collaboration of researchers and domain experts pushing the boundaries of what AI can know and prove

What you’ll do

Translate informal mathematical proofs into machine-verifiable Lean 4 formalizations to improve AI reasoning. Collaborate with AI researchers to design verification pipelines and analyze where automated provers fail.

Requirements

Requires a Master's degree or higher in Mathematics, Logic, or Theoretical Computer Science. Must have hands-on experience with Lean 4 or similar formal systems and a strong foundation in rigorous proof construction.

Other relevant skills

Identified from the job description. Confirm important requirements above.

• Lean 4
• Formal Verification
• Mathematical Proof Construction
• Automated Reasoning
• Type Theory
• Curry-Howard Correspondence
• Proof Decomposition
• Lemma Selection
• Coq
• Isabelle/HOL
• Agda
• Data Annotation
• AI Training Pipelines
• Logic
• Algebra
• Topology

Job areas

• Science & Research
• Technology
• Software
• Data & Analytics
• Engineering