Researcher - Lean 4 & Formal Proof Systems

Alignerr Corp.; Ireland; Remote; EUR 83,000 - 124,000; Full time

Job summary

Alignerr is seeking a Researcher to translate informal proofs into Lean 4 and related proof systems for AI training in mechanized mathematics. This remote hourly contract focuses on rigorous formalization and clear, machine-verifiable proofs across mathematical domains.

Candidate will analyze proofs, test automation boundaries, and collaborate to refine verification pipelines while contributing to advanced AI-driven formal reasoning research.

Qualifications

• Master's degree or higher in Mathematics, Logic, or Theoretical Computer Science.
• Strong proof writing and mathematical reasoning across algebra, analysis, topology, logic, or discrete math.
• Experience with Lean, Coq, Isabelle/HOL, or comparable systems.
• Ability to translate informal proofs into machine-verifiable formal proofs.
• Interest in AI training for formal reasoning and mechanized mathematics.

Responsibilities

• Translate informal mathematical proofs into Lean 4 (and related proof systems) with emphasis on clarity, structure, and correctness.
• Analyze proofs across domains to identify gaps, assumptions, and formalizable sub-structures.
• Construct formalizations that test the limits of existing proof assistants.
• Investigate where automated provers break down due to complexity or missing libraries.
• Develop readable, reproducible proof scripts aligned with best practices and idioms.
• Collaborate with researchers to design strategies for improving formal verification pipelines.
• Provide guidance on proof decomposition, lemma selection, and structure for formal models.
• Formalize classical proofs and compare machine-verifiable structures with textbook arguments.
• Surface deeper patterns or generalizations implicit in the original mathematics.

Skills

Mathematics

Logic

Theoretical Computer Science

Proof writing

Education

Master's degree or higher in Mathematics, Logic, Theoretical Computer Science

Tools

Lean (Lean 3/Lean 4)

Coq

Isabelle/HOL

Agda

Job description

Researcher — Lean 4 & Formal Proof Systems (AI Training)

About The Role

What if your deep mathematical expertise could directly shape how AI reasons about formal proofs — pushing the boundary of what machines can understand and verify? We're looking for mathematicians and formal verification specialists to translate sophisticated human-written proofs into Lean 4, working at the cutting edge of mechanized mathematics and AI research.

• 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 proofs across domains - identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test the limits of existing proof assistants, especially where automation struggles or fails
• Investigate and articulate where automated provers break down - due to complexity, missing lemmas, insufficient libraries, or other factors
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant 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
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• Surface deeper patterns or generalizations implicit in the original mathematics

Who You Are

• 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 algebra, analysis, topology, logic, or discrete mathematics
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems - Lean strongly preferred
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into clean, structured, machine-verifiable formal proofs
• Mathematically mature and comfortable working at the frontier of what proof assistants can currently express

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 stimulating work
• Contribute directly to advancing the capabilities of AI in formal reasoning and mathematics
• Potential for ongoing work and contract extension as new projects launch