Mathematical Formalization Specialist

Alignerr Corp.; United States; Remote; USD 83,000 - 152,000; Part time

Job summary

Alignerr invites a Mathematical Formalization Specialist to translate dense mathematical arguments into Lean formalizations for AI reasoning. This is a fully remote, hourly contract for mathematically mature specialists who thrive on precision, rigor, and elegant structure.

You will convert informal proofs into machine-verified Lean (and related systems), analyze proofs for gaps, and collaborate with AI researchers to improve theorem-proving tools while maintaining readable, reproducible scripts.

Qualifications

• Master’s degree or higher in Mathematics, Logic, or related field.
• Strong foundation in rigorous proof writing across algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean, Coq, Isabelle/HOL, or Agda (Lean strongly preferred).

Responsibilities

• Translate informal proofs into Lean formalizations with clarity 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.
• Collaborate with AI researchers to design 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.

Skills

Proof writing

Mathematical reasoning

Communication

Education

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

Tools

Lean (Lean 3/4)

Coq

Isabelle/HOL

Agda

Job description

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