Mathematical Formalization Specialist

Alignerr Corp.; Seattle (WA); Remote; USD 83,000 - 165,000; Part time

Job summary

Alignerr is seeking a Mathematical Formalization Specialist to translate informal proofs into Lean and related systems. You will work on machine-verifiable mathematics and contribute to parsing and structuring complex arguments for formal proof environments.

This is a fully remote hourly contract. You will collaborate with researchers, test proof strategies, and document clear, readable proof scripts while advancing the capabilities of formal verification pipelines.

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or closely related field.
• Hands-on experience with Lean (Lean 3 or Lean 4) or other proof systems like Coq, Isabelle/HOL, or Agda.
• Ability to translate informal mathematical arguments into clean, structured formal proofs.
• Strong communication skills to explain formalization decisions and edge cases.

Responsibilities

• Translate informal mathematical proofs into Lean (and related proof systems) with clarity and correctness.
• Analyze generic and domain-specific proofs to identify gaps and formalizable sub-structures.
• Construct formalizations that test the limits of existing proof assistants.
• Collaborate with researchers to refine strategies for improving formal verification pipelines.
• Develop readable, reproducible proof scripts aligned with proof assistant idioms.
• Provide guidance on proof decomposition and lemma selection for formal models.
• Investigate why automated provers break down and articulate the causes.

Skills

Lean / formal proof systems experience

Formal verification

Proof writing

Mathematics / Logic

Communication skills

Education

Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or closely related field

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About The Role

What if your deep mathematical expertise could directly shape how AI reasons, proves, and understands the world's most complex ideas? We're looking for mathematicians with hands-on experience in formal proof systems to help us map the frontier of machine-verifiable mathematics — working on problems that automated tools simply cannot yet solve on their own.

This is a fully remote, flexible contract role built for mathematicians who are passionate about precision, formal verification, and the future of mechanized reasoning.

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

What You'll Do

• Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and correctness
• Analyze generic and domain-specific proofs — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test 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 highly 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 why — complexity, missing lemmas, library gaps, and more

Must-Have

Who You Are

• 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 proof systems — Lean strongly preferred
• Genuine enthusiasm for formal verification, proof assistants, and mechanized mathematics
• Ability to translate dense, informal mathematical arguments into clean, structured formal proofs

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 where automated reasoning frequently requires manual scaffolding
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies

Sample Work You Might Do

• Formalize classical proofs and compare machine-verifiable structures against standard textbook arguments
• Build Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics
• Document where and why existing proof assistants fall short — and help advance the tools that will bridge those gaps

Why Join Us

• Work at the frontier of AI research alongside leading AI labs and research teams
• Fully remote and flexible — work on your own schedule, from anywhere
• Freelance autonomy with the structure of meaningful, intellectually stimulating tasks
• Contribute to high-integrity AI datasets that advance the reliability and reasoning capability of frontier models
• Potential for ongoing work and contract extension as new projects launch