Formal Verification Scientist (Lean 4 & Mathlib)

Alignerr Corp.; Birmingham; Remote; GBP 55,000 - 124,000; Part time

Job summary

Alignerr is seeking Formal Verification Scientists to translate advanced mathematical arguments into machine-verifiable Lean 4 proofs. You will work at the frontier of what proof assistants can express and automate, shaping how AI understands formal reasoning.

This fully remote, hourly contract invites mathematicians who love rigorous proof construction to tackle dense, elegant arguments and express them in machine-checkable form. Flexible hours and collaboration with researchers are included.

Qualifications

• Master's degree or higher in maths or CS theory.
• Experience with Lean, Coq, Isabelle/HOL, or similar proof systems.
• Ability to translate informal proofs into machine-verifiable Lean 4 proofs.

Responsibilities

• Translate informal proofs into Lean 4 formalizations.
• Analyze proofs to identify gaps and formalizable sub-structures.
• Push limits of proof assistants and automate where possible.
• Write readable, reproducible Lean scripts.
• Collaborate to improve verification pipelines.
• Guide proof decomposition and lemma selection.
• Explain why automated provers fail and document reasons.
• Create Lean proofs revealing deeper patterns.

Skills

Lean

Formal proof

Mathematical reasoning

Proof automation awareness

Education

Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or a closely related field

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your deep mathematical training could directly shape how AI understands and reasons about formal proof? We're looking for Formal Verification Scientists to translate advanced mathematical arguments into machine-verifiable Lean 4 proofs - working at the very frontier of what proof assistants can express, capture, and automate.

This is a fully remote, flexible contract role built for mathematicians who love rigorous proof construction and want to work on problems that matter. If you find satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify - this role was made for you.

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

What You'll Do

• Translate informal mathematical proofs into precise, machine-verifiable formalizations in Lean 4
• Analyze generic and domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that push the limits of existing proof assistants - especially where automated tools struggle or fail
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Provide guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Investigate where automated provers break down and clearly articulate why - complexity, missing lemmas, insufficient libraries, and beyond
• Create Lean proofs that surface 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
• Strong foundation in rigorous proof writing and mathematical reasoning across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or a comparable formal system - Lean strongly preferred
• Genuinely enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into clean, structured, formally correct proofs
• Mathematically mature problem-solver who appreciates precision, structural beauty, and the challenge of bridging gaps automated tools can't yet close

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, technically demanding work
• Contribute directly to how AI systems learn to reason about advanced mathematics
• Exposure to frontier LLM research and how formal verification intersects with AI training
• Potential for ongoing work and contract extension as new projects launch