Overview
Lean 4 Proof Engineer - Mathematical Formalization
Alignerr, Manchester, United Kingdom
Base pay
$70.00/hr - $150.00/hr
Location
Remote
Role overview
At Alignerr, we partner with the world’s leading AI research teams and labs to build and train cutting-edge AI models.
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.
* Sample work you might do: formalize classical proofs and compare machine-verifiable structures against textbook arguments; investigate where automated provers break down and explain why; create Lean proofs that reveal deeper patterns or generalizations.
Requirements
* 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.
Preferred
* Prior experience with data annotation, data quality, or evaluation systems
* 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
Ideal Candidate
* A mathematically mature problem-solver who enjoys working at the frontier of formal verification; someone who finds satisfaction in taking a dense, elegant human argument and expressing it in a form that a machine can understand. You appreciate precision, structural beauty, and the challenge of resolving gaps that automated tools cannot yet bridge.
Why join us
* Competitive pay and flexible remote work.
* Collaborate with a team working on cutting-edge AI projects.
* Exposure to advanced LLMs and how they’re trained.
* Freelance perks: autonomy, flexibility, and global collaboration.
* Potential for contract extension.
Application process
* Submit your resume
* Complete a short screening
* Project matching and onboarding
PS: Our team reviews applications daily. Please complete your AI interview and application steps to be considered for this opportunity.
Seniority level
* Entry level
Employment type
* Contract
Job function
* Management and Manufacturing
Industries
* Technology, Information and Internet
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