Mathematical Formalization Specialist (Lean / Formal Proof Systems)
About The Role
What if your deep mathematical expertise could directly shape the future of AI reasoning? We're looking for mathematicians with formal verification experience to translate advanced human-written proofs into machine-verifiable Lean formalizations — working at the very edge of what proof assistants can do today.
This is a fully remote, flexible contract role designed for mathematicians who find genuine satisfaction in precision, structure, and pushing the limits of mechanized reasoning.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: Flexible, task-based
What You'll Do
Translate informal mathematical proofs into Lean (Lean 3 or Lean 4) with a focus on clarity, correctness, and structural elegance
Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures
Construct formalizations that test and extend the limits of existing proof assistants
Collaborate with AI researchers to design and refine formal verification strategies
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
Investigate where automated provers break down and articulate why — helping map the frontier of formal verification
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 (strongly preferred), Coq, Isabelle/HOL, Agda, or a comparable formal proof system
Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
Able to take a dense, informal mathematical argument and express it precisely in a form a machine can verify
Self-directed and comfortable working independently on complex, open-ended problems
Nice to Have
Familiarity with type theory, the Curry–Howard correspondence, or proof automation tools
Experience contributing to large-scale formalization projects such as mathlib
Exposure to theorem provers in settings where automation frequently fails or requires manual scaffolding
Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies
Sample Work
Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments
Identify and articulate precisely where and why automated provers fail — missing lemmas, library gaps, complexity barriers
Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
Why Join Us
Work on genuinely cutting-edge AI research alongside leading labs — your contributions directly advance AI reasoning
Fully remote and asynchronous — work when and where it suits you
Freelance autonomy with meaningful, intellectually stimulating task-based work
Rare opportunity to work at the intersection of advanced mathematics and frontier AI development
Potential for ongoing work and contract extension as new formalization projects launch