Formal Verification Scientist (Lean 4 & Mathlib)

About The Role

What if your deep mathematical training could directly shape how AI understands and reasons about formal proof? We're looking for Formal Verification Scientists to translate advanced human-written mathematics into precise, machine-verifiable Lean 4 formalizations — helping map the very frontier of what modern proof assistants can express, capture, and automate.

This is a fully remote, flexible contract role built for mathematicians who are passionate about formal verification and eager to push the limits of mechanized mathematics.

• 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 a focus on clarity, correctness, and mathematical rigor
• Analyze proofs across domains — identifying hidden assumptions, gaps, and formalizable sub-structures
• Construct formalizations that test the limits of existing proof assistants, especially where automated tools struggle or fail
• Investigate where automated provers break down and articulate why — complexity, missing lemmas, library gaps, and beyond
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics

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 proof assistant — Lean 4 strongly preferred
• Able to translate dense, informal arguments into precise, structured formal proofs
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics

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 where automated reasoning frequently fails or requires manual scaffolding
• Prior experience with data annotation, data quality, or AI evaluation workflows
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies

Why This Role

You're not just writing proofs — you're working at the intersection of mathematics and artificial intelligence, helping determine what formal reasoning can and cannot yet do. This is rare, meaningful work that only a small number of people in the world are positioned to do well.

Why Join Us

• Work on cutting-edge AI projects alongside leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, high-impact work
• Contribute directly to how AI systems learn to reason about mathematics
• Potential for ongoing work and contract extension as new projects launch