Mathematical Formalization Specialist - Remote

Alignerr; San Francisco (CA); Remote; USD 68,880 - 206,640; Part time

Job summary

A leading AI partner is looking for a Mathematical Formalization Specialist to join their remote team. This role focuses on translating informal mathematical proofs into formal, machine-verifiable formats using Lean and other proof systems. Candidates should have a Master's degree in Mathematics or a related field and a strong background in rigorous proof construction and verification. The position offers competitive compensation ranging from $50 to $150 per hour, making it ideal for mathematically-minded individuals passionate about formal verification.

Qualifications

• Master’s degree or higher in Mathematics or related field.
• Strong foundation in rigorous proof writing and reasoning.
• Experience with formal proof languages, especially Lean.

Responsibilities

• Translate informal mathematical proofs into Lean.
• Analyze proofs, identifying gaps and assumptions.
• Collaborate with researchers to refine formal verification strategies.

Skills

Rigorous proof writing

Mathematical reasoning

Experience with Lean

Formal verification

Communication skills

Education

Master’s degree in Mathematics, Logic, Theoretical Computer Science

Tools

Lean 3

Lean 4

Coq

Isabelle/HOL

Agda

Job description

Mathematical Formalization Specialist – Remote

Join to apply for the Mathematical Formalization Specialist – Remote role at Alignerr

About Alignerr: Alignerr partners with leading AI labs to build expert‑driven workflows that improve model reasoning. We recruit top mathematicians and specialists to solve tasks where automated tools fail, advancing AI reliability, formalization, and high‑integrity dataset creation.

Role Overview: We are seeking a mathematician with deep training in rigorous proof construction and hands‑on experience with formal proof languages—especially Lean. This role sits at the intersection of mathematics and computer science, focusing on translating human‑written mathematical arguments into precise, machine‑verifiable formalizations. You will work on proofs that often lie beyond the current capabilities of automated provers, helping us map the frontier of what formal verification can express, capture, and automate.

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 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.

What You Bring – Must‑Have

• Master’s degree (or higher) in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete math.
• Hands‑on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems—with Lean strongly preferred.
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics.
• Ability to translate informal arguments into clean, structured formal proofs.

Nice‑to‑Have

• Familiarity with type theory, Curry–Howard correspondence, and proof automation tools.
• Experience with large‑scale formalization projects (e.g., mathlib).
• Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding.
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies.

Ideal Candidate

A mathematically mature problem‑solver who enjoys working at the frontier of formal verification—someone who finds satisfaction in taking a dense, elegant human argument and expressing it in a form that a machine can understand. You appreciate precision, structural beauty, and the challenge of resolving gaps that automated tools cannot yet bridge.

Sample Work You Might Do

• Formalize classical proofs and compare machine‑verifiable structures against textbook arguments.
• Investigate where automated provers break down, and articulate why (complexity, missing lemmas, insufficient libraries, etc.).
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics.

Compensation: $50 – $150 per hour