Mathematical Formalization Specialist (Lean / Formal Proof Systems)
About The Role
What if your mathematical expertise could directly shape the future of AI reasoning? We're looking for mathematicians with formal proof experience to translate advanced mathematical arguments into machine-verifiable Lean formalizations — working at the exact frontier where human mathematical intuition meets the limits of automated theorem proving.
This is a fully remote, flexible contract role for mathematically mature specialists who thrive on precision, structure, and intellectual challenge. If you find deep satisfaction in taking a dense, elegant proof and expressing it in a form a machine can verify — this role was built for you.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: Flexible
What You'll Do
Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness
Analyze domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
Construct formalizations that test the boundaries of existing proof assistants — especially where automated tools struggle or fail
Collaborate with AI researchers to design, refine, and evaluate formal verification strategies
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
Investigate where automated provers break down and articulate why — revealing complexity, missing lemmas, or library gaps
Who You Are
Hold a 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
Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
Able to translate informal mathematical arguments into clean, structured formal proofs with precision and clarity
Nice to Have
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 in contexts where automated reasoning frequently requires manual scaffolding
Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to research collaborators
Sample Work
Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments
Build Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
Map where automated provers fail and document the mathematical reasons why
Why Join Us
Work on cutting-edge AI projects alongside leading AI 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 capability of next-generation AI systems
Potential for ongoing work and contract extension as new projects launch