Mathematical Formalization Specialist (Lean ​/ Formal Proof Systems

About The Role

What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems - especially Lean - to tackle problems that sit beyond the reach of automated tools. This is a fully remote, flexible contract role at the intersection of mathematics and computer science. You'll work on genuinely hard problems, translating rigorous human arguments into machine-verifiable formalizations that help map the frontier of what proof assistants can express, capture, and automate.

• Organization:
  Alignerr
• Type:
  Hourly Contract
• Location:
  
  Remote
• Commitment:
  Flexible, task-based

• Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness
• Analyze proofs across mathematical domains - 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
• Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop clean, 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

• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate where automated provers break down - and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.)
• Write Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Hands-on experience with Lean (Lean 3 or Lean
  4), Coq, Isabelle/HOL, Agda, or comparable formal proof systems - Lean strongly preferred
• Genuine enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
• Ability to translate dense, informal mathematical arguments into clean, structured formal proofs

• 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
• Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies

You're a mathematically mature problem-solver who finds genuine satisfaction in taking a dense, elegant argument and expressing it in a form a machine can understand. You appreciate precision, structural beauty, and the intellectual challenge of resolving gaps that automated tools cannot yet bridge. You don't just do mathematics - you think carefully about how mathematics is done.

• Work on cutting-edge AI research projects alongside leading research labs
• Fully remote and flexible - work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually stimulating work
• Contribute directly to advancing the reliability and reasoning capabilities of next-generation AI
• Potential for ongoing work and contract extension as new projects launch