Mathematical Formalization Specialist

About the Role

What if your mathematical expertise could directly shape how AI reasons, verifies, and understands proofs at the highest level? We're looking for mathematicians with hands-on experience in formal proof systems — especially Lean — to help push the boundaries of what machine-verifiable mathematics can express and automate. This is a fully remote, flexible contract role working at the intersection of advanced mathematics and cutting-edge AI research. If you find deep satisfaction in translating elegant human arguments into precise, machine-checkable formalizations, this role was built for you.

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

Responsibilities

• Translate informal mathematical proofs into Lean (and related proof assistants) with an emphasis on clarity, structure, and correctness
• Analyze proofs across a range of domains — identifying 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 and evaluate strategies for improving formal verification pipelines
• Develop clean, readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and formal model structuring
• Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and more

Requirements

• 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) — experience with Coq, Isabelle/HOL, or Agda also valued
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal arguments into clean, well-structured formal proofs
• Mathematically mature — you thrive working at the frontier, not just within established territory

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 settings where automated reasoning frequently fails or requires manual scaffolding
• Strong communication skills for documenting formalization decisions, edge cases, and reasoning strategies

Sample Work

• Formalize classical or research-level proofs and compare machine-verifiable structures against informal textbook arguments
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
• Map the frontier of formal verification by identifying and analyzing the limits of current proof assistants

Benefits

• Work on genuinely frontier problems at the intersection of mathematics and AI
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually rigorous work
• Contribute to AI research that advances the reliability and reasoning capabilities of next-generation models
• Potential for ongoing work and contract extension as new projects launch