Mathematical Formalization Specialist

About the Role

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

Responsibilities

• 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

Requirements

• 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

Benefits

• 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