Lean 4 Proof Engineer - Mathematical Formalization

Alignerr Corp.; City of Edinburgh; Remote; GBP 83,000 - 138,000; Part time

Benefits offered by this job

Fully remote

Flexible hours

Freelance autonomy

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to translate dense mathematical proofs into machine-verifiable Lean formalizations. This fully remote contract role invites experts to shape future AI reasoning through formal verification, with 10–40 hours per week flexibility and autonomous project ownership.

Ideal candidates bring a strong mathematics background, hands-on Lean experience, and the ability to decompose complex arguments into clear, structured proofs suitable for machine verification.

Qualifications

• Master's degree or higher in Mathematics, Logic, or closely related field.
• Strong foundation in rigorous proof writing across algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean strongly preferred.

Responsibilities

• Translate informal mathematical proofs into Lean 4 (and related systems) with emphasis on clarity and correctness.
• Analyze proofs across domains, identify gaps, and formalizable sub-structures.
• Construct formalizations that test and expand the limits of existing proof assistants.
• Collaborate with AI researchers to improve formal verification pipelines.
• Develop readable, reproducible proof scripts aligned with Lean idioms.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques.
• Investigate where automated provers break down and explain why.

Skills

Lean 4

Lean 3

Coq

Isabelle/HOL

Agda

Formal verification

Proof writing

Mathematics

Education

Master's degree in Mathematics or related

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

Lean 4 Proof Engineer — Mathematical Formalization

About The Role

What if your deepest mathematical instincts could directly shape how the next generation of AI understands and reasons about formal proof? We're looking for expert mathematicians to translate rigorous human arguments into machine-verifiable Lean 4 formalizations — working at the very frontier of what proof assistants can do.

This is a fully remote, flexible contract role built for mathematicians who live and breathe formal reasoning. If you find satisfaction in taking a dense, elegant proof and expressing it in a form a machine can verify — this is your role.

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

What You'll Do

• Translate informal mathematical proofs into Lean 4 (and related systems) with a focus on clarity, structure, and correctness
• Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and expand the limits of existing proof assistants
• Collaborate with AI researchers to design and refine 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
• Investigate where automated provers break down — and articulate precisely why
• Create Lean proofs that reveal deeper patterns or generalizations implicit in classical 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 strongly preferred
• Genuinely passionate about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into clean, structured, machine-verifiable proofs
• Mathematically mature and comfortable working at the intersection of mathematics and computer science

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, or evaluation systems
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work on genuinely cutting-edge AI projects alongside world-leading research labs
• Fully remote and flexible — structure your hours around your life
• Freelance autonomy with the depth and meaning of serious mathematical work
• Rare opportunity to directly influence how AI systems reason about mathematics
• Potential for contract extension as projects evolve and expand