Lean 4 Proof Engineer - Mathematical Formalization

Alignerr Corp.; Charlotte (AR); Remote; USD 69,000 - 124,000; Full time

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to formalize mathematical arguments for AI training. You will translate informal proofs into precise, machine-verifiable Lean 4 formalizations with emphasis on clarity, structure, and correctness.

You will analyze proofs, construct robust formalizations, and collaborate with AI researchers to improve verification pipelines. This remote hourly contract offers 10–40 hours/week and potential project extensions.

Qualifications

• Master's degree or higher in Mathematics, Logic, or related field.
• Strong proof-writing and formalization skills across algebra, analysis, topology, logic.
• Experience with Lean or other proof assistants.
• Ability to translate informal proofs into machine-verifiable formalizations.

Responsibilities

• Translate informal mathematical proofs into precise, machine-verifiable Lean 4 formalizations, with an emphasis on clarity, structure, and correctness.
• Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that test the limits of existing proof assistants—especially where automated tools struggle or fail entirely.
• Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
• Develop readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
• Investigate where automated provers break down and articulate why—complexity, missing lemmas, insufficient libraries, and beyond.
• Reveal deeper patterns or generalizations implicit in the original mathematics through your formalizations.

Skills

Proof writing

Mathematical reasoning

Research collaboration

Communication

Education

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

Tools

Lean (Lean 3/4)

Coq

Isabelle/HOL

Agda

Job description

Lean 4 Proof Engineer — Mathematical Formalization (AI Training)

What if your mathematical training could directly shape how AI reasons, proves, and understands the deepest structures of mathematics? We're looking for Lean 4 Proof Engineers to formalize advanced mathematical arguments for cutting-edge AI research — working at the frontier of what proof assistants can express, verify, and automate.

This is a fully remote, flexible contract role built for mathematicians who think in rigorous proof and feel at home inside a formal system. If you find genuine satisfaction in taking a dense, elegant argument and expressing it in a form a machine can verify — this role was made for you.

• Organization: Alignerr
• Type: Hourly Contract
• Location: Remote
• Commitment: 10–40 hours/week

What You'll Do

• Translate informal mathematical proofs into precise, machine-verifiable Lean 4 formalizations, with an emphasis on clarity, structure, and correctness
• Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test the limits of existing proof assistants — especially where automated tools struggle or fail entirely
• Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers break down and articulate why — complexity, missing lemmas, insufficient libraries, and beyond
• Reveal deeper patterns or generalizations implicit in the original mathematics through your formalizations

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 comparable formal systems — Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal, human-written arguments into clean, structured, machine-verifiable proofs
• A mathematically mature problem‑solver who finds the frontier of formal verification genuinely exciting

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 fails or requires manual scaffolding
• Prior experience with data annotation, data quality evaluation, or AI training workflows
• Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies to research collaborators

Why Join Us

• Work directly on cutting‑edge AI projects alongside world‑leading research labs
• Fully remote and flexible — structure your hours around your life, not the other way around
• Freelance autonomy: choose your own pace, work asynchronously, and collaborate globally
• Contribute to work that sits at the genuine intersection of mathematics and AI — helping machines understand human reasoning at its most rigorous
• Potential for ongoing work and contract extension as new projects launch