Mathematical Formalization Specialist

Alignerr Corp.; New York (NY); Remote; USD 165,000 - 262,000; Part time

Job summary

Alignerr Corp. seeks a Mathematical Formalization Specialist to translate informal proofs into Lean and related systems, advancing machine-verifiable mathematics.

This remote hourly contract roles involves analyzing proofs, constructing formalizations, and collaborating with AI research teams to improve verification pipelines. The role emphasizes clarity, structure, and machine-verifiability, with strong Lean experience and a deep foundation in mathematics.

Qualifications

• Master's degree or higher in Mathematics, Logic, or related field.
• Hands-on experience with Lean 3/4 and at least one other proof system.
• Strong ability to formalize informal proofs for machine verification.

Responsibilities

• Translate informal proofs into Lean with emphasis on machine verifiability.
• Analyze domain proofs to identify gaps and formalizable sub-structures.
• Develop formalizations that push limits of proof assistants.
• Collaborate with researchers to improve verification pipelines.
• Create readable, reproducible proof scripts following best practices.
• Guide proof decomposition and lemma selection for formal models.
• Investigate where automated provers fail and explain why.

Skills

Proof writing

Formal verification

Attention to detail

Education

Master's in Mathematics/Logic/TCSE

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

Mathematical Formalization Specialist (Lean / Formal Proof Systems)

About The Role

What if your deep mathematical training could directly shape how AI reasons, verifies, and understands the most complex proofs in existence? 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. This is a fully remote, flexible contract role working alongside leading AI research labs. You'll be tackling problems that automated tools can't yet solve, operating at the true frontier of formal verification.

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: Flexible — work on your own schedule

What You'll Do

• Translate informal mathematical proofs into Lean (and related proof systems) with an emphasis on clarity, structure, and machine‑verifiability
• Analyze domain‑specific proofs to identify gaps, hidden assumptions, and formalizable sub‑structures
• Construct formalizations that test and extend the limits of existing proof assistants — especially where tools struggle or fail
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• 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 for formal models
• Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, insufficient libraries, and more

Who You Are

• Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Possess a strong foundation in rigorous proof writing across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Have hands‑on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable formal proof system — Lean strongly preferred
• Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
• Able to take a dense, elegant human argument and express it in a form a machine can verify
• Detail‑oriented and precise — you find satisfaction in resolving the gaps that automated tools cannot bridge

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 written communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work on genuinely cutting‑edge AI and mathematics research alongside leading research labs
• Fully remote and flexible — structure your work around your life, not the other way around
• Freelance autonomy with the substance of meaningful, high‑impact technical work
• Contribute directly to advancing the frontier of formal verification and AI reasoning capabilities
• Potential for ongoing work and contract extension as new projects launch