Formal Verification Scientist (Lean 4 & Mathlib)

Alignerr Corp.; Ireland; Remote; EUR 83,000 - 165,000; Part time

Job summary

Alignerr seeks Formal Verification Scientists to translate advanced mathematical arguments into Lean 4 proofs, at the intersection of rigorous math and AI research. This fully remote, flexible contract role targets mathematicians who love precision and frontier proof work.

Work remotely 10–40 hours weekly, collaborating with AI researchers to shape verification pipelines and machine-verifiable mathematical knowledge for AI systems.

Qualifications

• Master's degree or higher in Mathematics, Logic, Theoretical Computer Science, or related field
• Strong proof-writing foundation across algebra, analysis, topology, logic, or discrete math
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof assistant — Lean preferred
• Genuine enthusiasm for formal verification, proof assistants, and mechanized mathematics
• Ability to translate dense informal arguments into machine-verifiable formalizations

Responsibilities

• Translate informal mathematical proofs into clean Lean 4 formalizations
• Analyze proofs across domains to identify gaps and formalizable sub-structures
• Push boundaries of proof assistants on problems beyond current automation
• Collaborate with AI researchers to design formal verification pipelines
• Develop readable, reproducible proof scripts aligned with Lean idioms
• Provide guidance on proof decomposition, lemma selection, and structuring strategies
• Investigate why automated provers fail and articulate reasons clearly
• Uncover deeper patterns and generalizations in classical arguments

Skills

Lean proficiency

Formal proof writing

Mathematics depth

Independent problem solving

Communicating formal results

Proof automation awareness

Education

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

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

About The Role

What if your deep mathematical training could directly shape how AI reasons about truth, proof, and knowledge? We're looking for Formal Verification Scientists to translate advanced mathematical arguments into machine-verifiable Lean 4 proofs — working at the precise intersection of rigorous mathematics and cutting-edge AI research.

What if your deep mathematical training could directly shape how AI reasons about truth, proof, and knowledge? We're looking for Formal Verification Scientists to translate advanced mathematical arguments into machine-verifiable Lean 4 proofs — working at the precise intersection of rigorous mathematics and cutting-edge AI research.

This is a fully remote, flexible contract role designed for mathematicians who love precision and thrive at the frontier of what proof assistants can express, capture, and automate.

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

What You'll Do

• Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations
• Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Push the boundaries of existing proof assistants by working on problems that lie beyond current automation capabilities
• Collaborate with AI researchers to design and refine formal verification pipelines
• Develop readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring strategies for formal models
• Investigate where automated provers break down — and articulate precisely why
• Uncover deeper patterns and generalizations hidden within classical mathematical arguments

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 a comparable proof assistant — Lean strongly preferred
• Genuinely excited about formal verification, proof assistants, and the future of mechanized mathematics
• Able to take a dense, informal argument and express it precisely in a form a machine can verify
• Self-directed and comfortable working independently on complex, open-ended problems

Nice to Have

• Familiarity with type theory, the Curry-Howard correspondence, and proof automation tools
• Experience contributing to 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, quality evaluation, or AI training workflows
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies

Why Join Us

• Work directly on cutting-edge AI projects alongside leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the depth and challenge of meaningful, frontier-level work
• Gain rare exposure to how advanced LLMs are trained to reason about mathematics
• Contribute to a growing body of machine-verifiable mathematical knowledge that will shape AI for years to come
• Potential for ongoing work and contract extension as new projects launch