Lean 4 Proof Engineer - Mathematical Formalization

Alignerr; United States; On-site; USD 83,000 - 165,000; Part time

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to translate informal mathematics into machine-verifiable Lean proofs. This remote, hourly contract role offers flexible hours (10–40 per week) and the chance to push the boundaries of formal verification across diverse mathematical domains.

You will develop structured Lean formalizations, audit proofs for gaps or assumptions, and collaborate with researchers to advance proof strategies and automated reasoning tools.

Qualifications

• Master's degree or higher in Mathematics, Logic, or a related field.
• Strong foundation in rigorous proof writing across algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or similar proof systems — Lean 4 preferred.

Responsibilities

• Translate informal mathematical proofs into clean, structured, machine-verifiable Lean 4 formalizations.
• Analyze proofs across domains, identifying gaps, hidden assumptions, and formalizable sub-structures.
• Construct formalizations that test and extend the limits of existing proof assistants.
• Investigate where automated provers break down and articulate the underlying reasons.
• Collaborate with researchers to design and refine formal verification strategies.
• Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms.
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques.
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments.
• Create Lean proofs that reveal deeper patterns or generalizations in the original mathematics.

Skills

Lean 4

Formal verification

Mathematics

Proof writing

Education

Master's degree or higher in Mathematics

Tools

Lean 4

Coq/Isabelle/Agda

Job description

Lean 4 Proof Engineer — Mathematical Formalization

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

This is a fully remote, flexible contract role. If you live for rigorous proof construction and find satisfaction in the precision of formal systems, this is the role built for you.

• 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
• Construct formalizations that test and extend the limits of existing proof assistants
• Investigate where automated provers break down and articulate the underlying reasons — complexity, missing lemmas, library gaps, and more
• Collaborate with researchers to design and refine formal verification strategies
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques
• Formalize classical proofs and compare machine-verifiable structures against textbook arguments
• 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 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 comparable proof systems — Lean 4 strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate informal arguments into clean, well-structured formal proofs with precision and clarity

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

Why Join Us

• Work on cutting‑edge AI research projects alongside leading labs and research teams
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy with intellectually stimulating, frontier‑level work
• Contribute directly to how AI systems understand and reason about advanced mathematics
• Potential for ongoing work and contract extension as new projects launch