Lean 4 Proof Engineer - Mathematical Formalization

Alignerr Corp.; Glasgow; À distance; GBP 83 000 - 165 000; Temps partiel

Résumé du poste

Alignerr is seeking a Lean 4 Proof Engineer to formalize advanced mathematics into machine-verified Lean code. This remote contract role focuses on precision, structure, and sound argumentation, translating informal proofs into formal scripts and exploring the limits of proof assistants.

You will work with AI researchers to improve verification pipelines and contribute to high-impact formalization projects in a fully remote setting.

Qualifications

• Master's degree or higher in Mathematics, Logic, or theoretical computer science.
• Strong foundation in rigorous proof writing across algebra, analysis, topology, logic, or discrete mathematics.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems.
• Ability to translate informal proofs into machine-verifiable Lean formalizations.
• Interest in AI research and collaboration on verification pipelines.

Responsabilités

• Translate informal proofs into Lean 4 formalizations with emphasis on correctness and clarity.
• Analyze proofs to identify assumptions, gaps, and sub-structures.
• Construct formalizations that test and expose the limits of existing proof assistants.
• Collaborate with AI researchers to design and evaluate verification strategies.
• Develop readable, reproducible Lean scripts aligned with formal practices.
• Guide proof decomposition, lemma selection, and structuring techniques for formal models.
• Investigate where automated provers break down and explain why.
• Create Lean proofs that reveal deeper patterns in the original mathematics.

Connaissances

Formal proofs

Mathematical reasoning

Critical thinking

Collaboration

Formation

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

Outils

Lean (Lean 3/4)

Coq

Isabelle/HOL

Agda

Description du poste

Lean 4 Proof Engineer — Mathematical Formalization

About The Role

What if your deep mathematical training could directly shape the future of AI — and help machines understand the most rigorous arguments the human mind can produce?

We're looking for expert mathematicians with hands-on experience in formal proof systems to translate advanced mathematical reasoning into machine-verifiable Lean 4 code. This role sits at the frontier of what proof assistants can express, capture, and automate — and you'll be the one mapping that frontier.

This is a fully remote, flexible contract role for mathematicians who care deeply about precision, structure, and the art of formal argumentation.

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

What You'll Do

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on correctness and clarity
• Analyze proofs across domains — identifying hidden assumptions, logical gaps, and formalizable sub-structures
• Construct formalizations that test and expose the limits of existing proof assistants
• Collaborate with AI researchers to design and evaluate strategies for improving formal verification pipelines
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Guide proof decomposition, lemma selection, and structuring techniques for formal modelsInvestigate where automated provers break down — and articulate precisely why
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics

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 systems — Lean 4 strongly preferred
• Thrive at the intersection of mathematics and formal computer science
• Take satisfaction in translating dense, elegant human arguments into forms a machine can fully verify
• Appreciate precision, structural beauty, and the challenge of resolving gaps that automated tools cannot yet bridge

Nice to Have

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
• Experience contributing to large-scale formalization projects (e.g., Mathlib)
• Exposure to theorem provers where automated reasoning frequently fails or requires manual scaffolding
• Prior experience with data annotation, quality evaluation, or AI training workflows
• Strong communication skills for articulating formalization decisions, edge cases, and proof strategies

Why Join Us

• Work directly on cutting-edge AI research alongside leading labs and researchers
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually rigorous work
• Operate at the frontier of mechanized mathematics — pushing what formal verification can achieve
• Potential for ongoing work and contract extension as new projects launch