Mathematical Formalization Specialist

Mathematical Formalization Specialist (Lean / Formal Proof Systems)About The RoleWhat if your mathematical expertise could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems to tackle problems that sit beyond the reach of automated tools - translating rigorous human arguments into machine-verifiable Lean proofs at the frontier of what formal verification can express.
This is a fully remote, flexible contract role designed for mathematicians who love precision, structural elegance, and the challenge of pushing proof assistants to their limits.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: Flexible hours, work on your own schedule
What You'll Do
Translate informal mathematical proofs into Lean (and related proof systems) with a focus on clarity, correctness, and structure
Analyze domain-specific and general proofs to identify gaps, hidden assumptions, 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, refine, and evaluate strategies for improving formal verification pipelines
Develop 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
Investigate where automated provers break down and articulate the underlying reasons - complexity, missing lemmas, insufficient libraries, and more
Who You Are
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 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, informal mathematical argument and express it in a form a machine can verify
Comfortable working independently and asynchronously in a remote environment
Nice to Have
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 manual scaffolding
Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies to research collaborators
Why Join Us
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 advancing AI reliability, formal reasoning, and high-integrity dataset creation
Work at the true frontier of mathematics and computer science - on problems no automated tool can yet solve
Potential for ongoing work and contract extension as new projects launch
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