Formal Verification Scientist (Lean 4 & Mathlib)

Formal Verification Scientist (Lean 4 & Mathlib)

About the Role

What if your deep mathematical expertise could directly shape how AI understands and reasons about formal proof? We're looking for mathematicians with hands-on experience in formal verification to translate rigorous human-written arguments into machine-verifiable proofs — working at the absolute frontier of what modern proof assistants can express and automate.

This is a fully remote, flexible contract role built for mathematically mature problem-solvers who find satisfaction in the precision and structural beauty of formal proof construction.

• 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 a focus on clarity, correctness, and structure
• Analyze proofs across a range of domains, identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that push the limits of existing proof assistants — especially where automation struggles or fails
• Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop clean, readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate and clearly articulate where automated provers break down — whether due to complexity, missing lemmas, or library gaps
• Create Lean proofs that reveal 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 comparable proof systems — Lean strongly preferred
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal arguments into clean, structured formal proofs with precision and care

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 evaluation systems
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to collaborators

Why Join Us

• Work on cutting-edge AI projects alongside leading research labs and AI teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, high-impact technical work
• Operate at the frontier of formal verification and contribute to how AI learns to reason mathematically
• Potential for ongoing work and contract extension as new projects launch