Formal Verification Scientist; Lean 4 & Mathlib

What if your deepest mathematical knowledge could directly shape how AI reasons about truth, proof, and logic? We're looking for Formal Verification Scientists to translate advanced human-written mathematics into machine-verifiable Lean proofs — helping map the frontier of what AI can understand, verify, and automate.

This is a fully remote, flexible contract role for mathematicians who live and breathe rigorous proof and want to work at the cutting edge of formal verification and AI research.

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

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and mathematical elegance
• Analyze proofs across domains — algebra, analysis, topology, logic, and beyond — identifying gaps, hidden assumptions, and formalizable sub-structures
• Push the boundaries of existing proof assistants by constructing formalizations where automated tools struggle or fail
• Investigate where automated provers break down and articulate precisely why — missing lemmas, library gaps, complexity barriers
• Develop highly readable, reproducible proof scripts aligned with Mathlib conventions and best practices
• Collaborate with AI researchers to design and refine formal verification pipelines
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
• Provide expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models

• 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
• Genuinely excited by formal verification, proof assistants, and the future of mechanized mathematics
• Able to bridge the gap between informal mathematical intuition and precise formal structure
• Thrive working independently on deep, intellectually demanding problems

• Experience with large-scale formalization projects such as Mathlib
• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
• Exposure to theorem provers in settings where automated reasoning frequently requires manual scaffolding
• Prior experience with data annotation, evaluation systems, or proof quality assessment
• Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies

This isn't routine annotation work. You'll be operating at the true frontier — taking dense, elegant mathematical arguments and expressing them in forms a machine can verify. Every proof you formalize contributes directly to how the next generation of AI systems understands and reasons about mathematics.

• Work on research-grade problems that matter at the intersection of mathematics and AI
• Fully remote and flexible — structure your own schedule around deep work
• Freelance autonomy with the intellectual depth of a research environment
• Collaborate with world-class AI research teams and labs
• Potential for ongoing work and contract extension as projects evolve