Applied Formal Methods Researcher (Lean 4)

About The Role What if your deep mathematical training could directly shape how AI reasons about proofs — pushing the boundaries of what machines can verify, understand, and automate? We're looking for mathematicians with hands-on experience in formal proof systems to translate rigorous human arguments into machine-verifiable Lean 4 formalizations. You'll work at the cutting edge of AI research, helping map the frontier of automated reasoning and formal verification. This is a fully remote, flexible contract role designed for mathematically mature problem-solvers who find satisfaction in the precise, structural beauty of formal proof.

• 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 both 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 AI 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 expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers break down — and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.)
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments

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 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 a comparable formal proof system — Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate complex informal arguments into clean, structured formal proofs independently
• Thrive working at the frontier — you're energized by problems that automated tools can't yet solve

Nice to Have

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
• Experience contributing to large-scale formalization projects (e.g., mathlib)
• Exposure to theorem provers where automated reasoning frequently requires manual scaffolding
• Prior experience with data annotation, evaluation systems, or AI training workflows
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work directly with leading AI research labs on cutting-edge projects at the intersection of mathematics and AI
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with meaningful, intellectually stimulating work
• Gain exposure to advanced LLMs and the training pipelines that shape them
• Contribute to work that defines the future of mechanized mathematics and AI reasoning
• Potential for ongoing work and contract extension as new projects launch