Formal Verification Scientist (Lean 4 & Mathlib)

Alignerr Corp.; Cambridge; Remote; GBP 55,000 - 117,000; Full time

Job summary

Alignerr is seeking a Formal Verification Scientist to translate advanced mathematics into machine-verifiable knowledge and to push the boundaries of proof assistants. This is a fully remote hourly contract designed for mathematicians who enjoy rigorous proof and mechanized mathematics.

You will work on translating informal arguments into Lean-based formal proofs, collaborate with researchers, and develop highly readable proof scripts following Lean idioms.

Qualifications

• Hold a Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
• Strong foundations in rigorous proof writing and mathematical reasoning 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 proof systems) with clarity, structure, and correctness.
• Analyze generic and domain-specific proofs, identify gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that test the limits of existing proof assistants, especially where automation struggles.
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines.
• Develop readable, reproducible proof scripts aligned with Lean idioms and mathematical best practices.
• Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments.
• Investigate where automated provers break down and articulate why (complexity, missing lemmas, libraries).
• Create Lean proofs that reveal deeper patterns or generalizations implicit in the original mathematics.

Job description

About The Role

What if your deep mathematical training could directly shape how AI systems understand and reason about formal proof? We're looking for Formal Verification Scientists to translate advanced mathematics into machine-verifiable knowledge - working at the frontier of what proof assistants can express, capture, and automate.

About The Role

What if your deep mathematical training could directly shape how AI systems understand and reason about formal proof? We're looking for Formal Verification Scientists to translate advanced mathematics into machine-verifiable knowledge - working at the frontier of what proof assistants can express, capture, and automate.

This is a fully remote, flexible contract role designed for mathematicians who are passionate about rigorous proof and the future of mechanized mathematics. If you find satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify, 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 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 automated 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 Lean idioms
• Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Investigate where automated provers break down and articulate why - complexity, missing lemmas, insufficient libraries, and more
• 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
• Have a strong foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete math
• Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems - Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal mathematical arguments into clean, structured formal proofs
• Naturally detail-oriented, precise, and comfortable working independently

Nice to Have

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
• Experience with 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 cutting-edge AI projects alongside leading research labs
• Fully remote and flexible - work when and where it suits you
• Freelance autonomy with the structure of meaningful, intellectually demanding work
• Contribute directly to the frontier of formal verification and AI reasoning research
• Potential for ongoing work and contract extension as new projects launch