Formal Verification Scientist; Lean 4 & Mathlib

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

This is a fully remote, flexible contract role ideal for mathematicians who live at the intersection of rigorous proof construction and cutting-edge computer science.

• Organization:
  Alignerr
• Type:
  Hourly Contract
• Location:
  
  Remote
• Commitment: 10–40 hours/week

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with an emphasis on clarity, structure, and correctness
• Analyze 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 entirely
• 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 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 articulate where automated provers break down — due to complexity, missing lemmas, or insufficient libraries
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

• 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 comparable systems — Lean 4 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal mathematical arguments into clean, structured, machine‑verifiable proofs
• Mathematically mature and energized by working at the frontier — where automated tools run out and human insight takes over

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

• Work on cutting‑edge AI research projects alongside leading AI labs and research teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Contribute directly to expanding the frontier of formal verification and mechanized mathematics
• Gain rare exposure to how advanced AI models are trained on mathematical reasoning
• Potential for ongoing work and contract extension as new projects launch