Lean 4 Proof Engineer - Mathematical Formalization

Alignerr; Birmingham; Remote; GBP 83,000 - 152,000; Part time

Benefits offered by this job

Remote work

Flexible hours

Contractor autonomy

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to translate rigorous mathematical arguments into machine-verifiable formalizations. You will work at the edge of what proof assistants can express, ensuring correctness, clarity, and reproducibility in Lean 4 formalizations.

The role is a fully remote, hourly contract for mathematicians who value precision, structure, and the future of mechanized mathematics. Expect 10-40 hours per week with flexible scheduling and collaboration with AI researchers.

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Rigorous proof writer with deep experience across areas such as algebra, analysis, topology, logic, or discrete mathematics.
• Hands-on practitioner with Lean (Lean 3 or Lean 4), with strong preference for Lean 4 experience.
• Genuinely excited about formal verification, proof assistants and the frontier of mechanized mathematics.
• Able to take dense, informal mathematical arguments and render them into precise, structured formal proofs.
• Self-directed and comfortable working independently in an asynchronous environment.

Responsibilities

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations - with a focus on correctness, clarity, and reproducibility.
• Analyze proofs across domains to identify hidden assumptions, logical gaps, and formalizable substructures.
• Construct formalizations that probe and stress-test the limits of existing proof assistants.
• Investigate where automated provers break down - and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.).
• Collaborate with AI researchers to design and refine formal verification pipelines.
• Apply expert judgment in proof decomposition, lemma selection, and structuring strategies.
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics.
• Compare machine-verifiable structures against classical textbook arguments.

Skills

Lean experience

Proof writing

Formal verification

Independent work

Mathematics background

Education

Master's degree or higher in Mathematics/Logic/Theoretical CS

Tools

Coq/Isabelle/Agda

Job description

Lean 4 Proof Engineer - Mathematical Formalization

About The Role

What if your deep mathematical training could directly shape how the world's most advanced AI systems reason about proofs? We're looking for Lean 4 Proof Engineers to translate rigorous mathematical arguments into machine-verifiable formalizations - working at the very edge of what modern proof assistants can express and automate.

This is a fully remote, flexible contract role designed for mathematicians who care about precision, structure, and the future of mechanized mathematics.

• 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 a focus on correctness, clarity, and reproducibility
• Analyze proofs across domains to identify hidden assumptions, logical gaps, and formalizable substructures
• Construct formalizations that probe and stress-test the limits of existing proof assistants
• Investigate where automated provers break down - and articulate precisely why (complexity, missing lemmas, insufficient libraries, etc.)
• Collaborate with AI researchers to design and refine formal verification pipelines
• Apply expert judgment in proof decomposition, lemma selection, and structuring strategies
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
• Compare machine-verifiable structures against classical textbook arguments

Who You Are

• Holder of a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Rigorous proof writer with deep experience across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Hands‑on practitioner with Lean (Lean 3 or Lean 4), with strong preference for Lean 4 experience
• Genuinely excited about formal verification, proof assistants and the frontier of mechanized mathematics
• Able to take dense, informal mathematical arguments and render them into precise, structured formal proofs
• Self‑directed and comfortable working independently in an asynchronous environment

Nice to Have

• Familiarity with Coq, Isabelle/HOL, Agda, or other interactive theorem provers
• Knowledge of type theory, the Curry-Howard correspondence, and proof automation tools
• Experience contributing to large-scale formalization projects such as Mathlib
• Exposure to contexts where automated reasoning regularly fails or requires significant manual scaffolding
• Prior experience with data annotation, evaluation systems, or AI training pipelines
• Strong written communication skills for documenting formalization decisions, edge cases, and proof strategies

Why Join Us

• Work directly with leading AI research labs on some of the most technically demanding problems in formal mathematics
• Fully remote and flexible - structure your hours to fit your life
• Freelance autonomy with the depth and purpose of meaningful, frontier-level work
• Rare opportunity to work where mathematics, computer science, and AI training genuinely intersect
• Potential for ongoing work and contract extension as new projects launch