Lean 4 Proof Engineer - Mathematical Formalization

Alignerr; Chicago (IL); Remote; USD 69,000 - 165,000; Full time

Job summary

Alignerr Corp. seeks a Lean 4 Proof Engineer to translate advanced mathematical arguments into machine-verifiable Lean formalizations. You will work remotely, rigorously structuring proofs across algebra, analysis, topology, and logic, while exploring the limits of current proof assistants.

The role emphasizes collaboration with AI researchers, clear proof scripts, and scalable formalization practices in a flexible, hourly contract with 10–40 hours per week.

Qualifications

• Master's degree or higher in mathematics, logic, or related field.
• Strong proof-writing and rigorous reasoning across core areas.
• Hands-on experience with Lean (3 or 4), Coq, Isabelle/HOL or Agda.

Responsibilities

• Translate informal proofs into Lean formalizations with correctness and clarity.
• Analyze proofs across algebra, analysis, topology, logic, and discrete math.
• Construct formalizations to test limits of proof assistants.
• Investigate why automated provers fail and document findings.
• Collaborate with AI researchers to improve verification pipelines.
• Develop readable, reproducible Lean proofs and idioms.
• Offer guidance on lemma selection and structuring techniques.

Skills

Lean experience

Coq familiarity

Isabelle/HOL

Agda

Proof writing

Education

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

Tools

Mathlib

Job description

Lean 4 Proof Engineer — Mathematical Formalization

What if your mathematical expertise could directly shape how AI reasons, proves, and understands the deepest structures of formal logic? We're looking for Lean 4 Proof Engineers to translate advanced mathematical arguments into precise, machine-verifiable formalizations — working at the absolute frontier of what modern proof assistants can do.

This is a fully remote, flexible contract role built for mathematicians who love rigor, structure, and the challenge of making a machine understand what a human mind intuits.

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

What You'll Do

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on correctness and clarity
• Analyze proofs across domains — algebra, analysis, topology, logic, discrete math — and identify hidden assumptions, gaps, and formalizable sub-structures
• Construct formalizations that test and expose the limits of existing proof assistants, especially where automation breaks down
• Investigate why automated provers fail on specific problems — complexity, missing lemmas, insufficient libraries — and document your findings
• Collaborate with AI researchers to design, refine, and evaluate strategies for improving formal verification pipelines
• Develop readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models

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 and mathematical reasoning across core areas
• Have hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable systems — Lean 4 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to bridge the gap between informal human arguments and precise machine-verifiable structure
• Thrive working independently on technically demanding problems with real research impact

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 where automated reasoning frequently fails or requires manual scaffolding
• Prior experience with data annotation, data quality, or AI evaluation systems
• Strong written communication skills for explaining formalization decisions and reasoning strategies

The Ideal Candidate

You're a mathematically mature problem-solver who finds deep satisfaction in taking a dense, elegant human argument and expressing it in a form a machine can verify. You appreciate precision, structural beauty, and the intellectual challenge of resolving gaps that automated tools cannot yet bridge. You're energized by working at the edge of what formal verification can express — and you want that work to matter for the future of AI.

Why Join Us

• Work on cutting-edge AI projects alongside world‑leading research labs
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with the structure of meaningful, high‑impact technical work
• Gain direct exposure to how advanced AI models are trained and evaluated
• Potential for ongoing work and contract extension as new projects launch