Formal Verification Scientist (Lean 4 & Mathlib)

About The Role

What if your deep mathematical training could directly shape how AI reasons about truth, proof, and knowledge? We're looking for Formal Verification Scientists to translate advanced human mathematics into machine-verifiable Lean 4 proofs — working at the very frontier of what automated proof assistants can express and reason about.

This is a fully remote, flexible contract role built for mathematicians who are passionate about rigorous proof, formal systems, and the future of mechanized mathematics. If you find satisfaction in taking a dense, elegant argument and expressing it with the precision a machine can verify, this role was made for you.

• 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 proofs across domains, identifying hidden assumptions, gaps, and formalizable sub-structures
• Push the boundaries of existing proof assistants by working on problems where automated tools struggle or fail entirely
• Investigate and articulate why automated provers break down — whether due to complexity, missing lemmas, or insufficient library coverage
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Uncover deeper patterns and generalizations implicit in original mathematical arguments
• Collaborate with AI researchers to design, refine, and evaluate formal verification pipelines
• Provide guidance on proof decomposition, lemma selection, and structuring strategies for formal models

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 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 proof assistant — Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into well-structured, machine-verifiable formal proofs
• Mathematically mature — you appreciate precision, structural beauty, and the challenge of bridging human and machine reasoning

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 manual scaffolding
• Prior experience with data annotation, evaluation systems, or data quality workflows
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work on cutting-edge AI projects alongside leading research labs and teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually rigorous work
• Contribute directly to how AI understands and reasons about advanced mathematics
• Gain exposure to frontier large language models and how formal reasoning shapes their training
• Potential for ongoing work and contract extension as new projects launch