Mathematical Formalization Specialist

What if your deep mathematical expertise could directly shape the future of AI reasoning? We're looking for mathematicians who love rigorous proof and formal verification to help us map the frontier of what machine-verifiable mathematics can express - and push it further.

This is a fully remote, flexible contract role working with leading AI research labs. If you've spent years building intuition for proof structure, love the challenge of translating human arguments into formal systems, and have hands-on experience with Lean or similar proof assistants, this role was made for you.

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

• Translate informal mathematical proofs into Lean (Lean 3 or Lean
  4) with an emphasis on clarity, structure, and correctness
• Analyze complex proofs across domains, identifying hidden assumptions, gaps, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants - especially where automated tools struggle or fail
• Collaborate with researchers to design and refine strategies for improving formal verification pipelines
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Advise on proof decomposition, lemma selection, and structuring techniques for formal models

• 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 (strongly preferred), Coq, Isabelle/HOL, Agda, or comparable formal proof systems
• Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, elegant mathematical arguments into clean, structured formal proofs
• Thrive working independently on intellectually demanding, open-ended problems

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling
• Experience with large-scale formalization projects (e.g., mathlib)
• Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
• Ability to clearly articulate formalization decisions, edge cases, and reasoning strategies

• Formalize classical theorems and compare machine-verifiable structures against textbook arguments
• Investigate where automated provers break down and articulate exactly why - missing lemmas, library gaps, complexity limits
• Write Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics

• Work on genuinely frontier problems at the intersection of mathematics and AI
• Fully remote and asynchronous - work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Collaborate with leading AI labs and researchers pushing the boundaries of machine reasoning
• Potential for ongoing work and contract extension as new projects launch