Mathematical Formalization Specialist

What if your deep mathematical training could directly shape how AI reasons, verifies, and understands the most complex proofs in existence? We're looking for mathematicians with hands‑on experience in formal proof systems — especially Lean — to help push the boundaries of what machine‑verifiable mathematics can express. This is a fully remote, flexible contract role working alongside leading AI research labs.

You'll be tackling problems that automated tools can't yet solve, operating at the true frontier of formal verification.

• Organization:
  Alignerr
• Type:
  Hourly Contract
• Location:
  
  Remote
• Commitment:
  Flexible — work on your own schedule

• Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and machine‑verifiability
• Analyze domain‑specific proofs to identify gaps, hidden assumptions, and formalizable sub‑structures
• Construct formalizations that test and extend the limits of existing proof assistants — especially where tools struggle or fail
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and more

• 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 formal proof system — Lean strongly preferred
• Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
• Able to take a dense, elegant human argument and express it in a form a machine can verify
• Detail‑oriented and precise — you find satisfaction in resolving the gaps that automated tools cannot bridge

• 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 requires manual scaffolding
• Strong written communication skills for explaining formalization decisions, edge cases, and reasoning strategies

• Work on genuinely cutting‑edge AI and mathematics research alongside leading research labs
• Fully remote and flexible — structure your work around your life, not the other way around
• Freelance autonomy with the substance of meaningful, high‑impact technical work
• Contribute directly to advancing the frontier of formal verification and AI reasoning capabilities
• Potential for ongoing work and contract extension as new projects launch