Mathematical Formalization Specialist - Remote

Alignerr; Boston (MA); Remote; USD 68,880 - 206,640; Full time

Job summary

A forward-thinking mathematics firm is seeking a Mathematical Formalization Specialist to work remotely. In this role, you will translate informal mathematical proofs into structured formal proofs using Lean and related systems. A Master’s degree in Mathematics or a related field is required, along with hands-on experience in proof languages. The ideal candidate should have a strong foundation in rigorous proof writing and a deep enthusiasm for formal verification. This position offers competitive hourly pay ranging from $50 to $150.

Qualifications

• Deep training in rigorous proof construction.
• Hands-on experience with formal proof languages.
• Ability to translate informal arguments into clean formal proofs.

Responsibilities

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

Skills

Rigorous proof writing

Mathematical reasoning

Experience with Lean

Formal verification enthusiasm

Education

Master’s degree in Mathematics or related field

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

Mathematical Formalization Specialist - Remote

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.

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.

$50 - $150 an hour