Lean 4 Proof Engineer - Mathematical Formalization

Alignerr Corp.; Cambridge; Remote; GBP 83,000 - 165,000; Part time

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to translate informal mathematical proofs into machine-checkable formalizations. The role emphasizes rigorous proof construction, leveraging Lean 4 and related proof systems.

Remote contract, 10–40 hours per week, with collaboration across researchers to advance AI-driven formal verification workflows. You will develop readable proof scripts, identify gaps in existing libraries, and help extend formalization capabilities for complex mathematical

Qualifications

• Master's degree or higher in Mathematics, Logic, or related field.
• Strong proof-writing and formalization skills.
• Hands-on experience with Lean/Coq/Isabelle/HOL/Agda.
• Ability to translate informal proofs into machine-checkable form.

Responsibilities

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with emphasis on clarity, structure, and correctness
• Analyze domain-specific and general proofs, identifying hidden assumptions, logical gaps, and formalizable sub-structures
• Construct formalizations that test and extend the capabilities of existing proof assistants — especially where automated tools struggle or fail
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop readable, reproducible proof scripts that align with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers break down and articulate root causes — complexity, missing lemmas, library gaps, and beyond
• Uncover deeper patterns or generalizations implicit in the original mathematics through formal expression

Skills

Proof writing

Formal verification

Lean 4

Research collaboration

Education

Master's degree or higher in Mathematics/CS

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

Lean 4 Proof Engineer — Mathematical Formalization (AI Training)

About The Role

What if your deep mathematical training could directly shape how AI reasons about formal proofs — and help push the boundaries of what machines can understand and verify? We're looking for mathematicians with serious proof-writing chops and hands-on experience with formal proof systems to work on one of the most intellectually demanding challenges in AI today: translating complex human mathematical arguments into machine-verifiable formalizations using Lean 4. This is a fully remote, flexible contract role. If you live at the intersection of rigorous mathematics and formal verification — and you find satisfaction in the precision of making a dense, elegant argument machine-checkable — this role was built for you.

• 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 proof systems) with emphasis on clarity, structure, and correctness
• Analyze domain-specific and general proofs, identifying hidden assumptions, logical gaps, and formalizable sub-structures
• Construct formalizations that test and extend the capabilities of existing proof assistants — especially where automated tools struggle or fail
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop readable, reproducible proof scripts that align with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers break down and articulate root causes — complexity, missing lemmas, library gaps, and beyond
• Uncover deeper patterns or generalizations implicit in the original mathematics through formal expression

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
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal mathematical arguments into clean, well-structured formal proofs with precision and care

Nice to Have

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tooling
• Experience contributing to large-scale formalization projects such as Mathlib
• Exposure to theorem provers in settings where automated reasoning frequently fails or requires significant manual scaffolding
• Prior experience with data annotation, data quality evaluation, or AI training workflows
• Strong written communication skills for explaining formalization decisions, edge cases, and reasoning strategies to collaborators

Why Join Us

• Work at the absolute frontier of formal mathematics and AI research
• Collaborate with world-leading AI research teams and labs on genuinely hard problems
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with meaningful, intellectually stimulating work
• Contribute to shaping how AI systems understand, generate, and verify mathematical reasoning
• Potential for ongoing work and contract extension as new projects launch