Lean 4 Proof Engineer - Mathematical Formalization

Alignerr Corp.; Ireland; Remote; EUR 14,000 - 55,000; Part time

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to translate rigorous mathematics into machine-verifiable formalizations. You will work remotely on proofs, ensuring clarity and correctness, and push the limits of current proof assistants in AI training contexts.

The role requires an advanced degree in mathematics and hands-on Lean experience, with collaboration across AI researchers and mathematicians to refine verification pipelines.

Qualifications

• Advanced degree in mathematics or closely related field.
• Strong background in algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean (3 or 4) required.

Responsibilities

• Translate informal proofs into Lean 4 formalizations.
• Analyze proofs for gaps and formalizable substructures.
• Construct machine-verifiable formalizations pushing prover limits.
• Collaborate with AI researchers to refine verification strategies.
• Develop readable, reproducible Lean scripts following best practices.
• Guide proof decomposition and lemma selection for formal models.
• Formalize classical and advanced proofs and compare with textbook arguments.
• Explain where automated provers fail and map paths forward.

Skills

Proof construction

Formal reasoning

Independent work

Mathematical communication

Education

Master's or PhD in Mathematics

Tools

Lean

Coq

Isabelle/HOL

Agda

Job description

Lean 4 Proof Engineer — Mathematical Formalization (AI Training)

What if your deep mathematical expertise could directly influence how the world's most advanced AI systems reason, prove, and think? We're looking for Lean 4 Proof Engineers to translate rigorous human mathematics into machine-verifiable formalizations — working at the precise frontier where formal verification meets cutting-edge AI research.

This is a fully remote, flexible contract role built for mathematicians who find beauty in precision and satisfaction in expressing dense, elegant arguments in a form a machine can verify and learn from.

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

What You'll Do

• Translate informal mathematical proofs into Lean 4 — emphasizing clarity, correctness, and structural elegance
• Analyze proofs across domains, identifying hidden assumptions, logical gaps, and formalizable substructures
• Construct formalizations that push proof assistants to their limits — especially where automated tools struggle or fail entirely
• Collaborate with AI researchers to design and refine formal verification strategies and pipelines
• Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Formalize classical and advanced proofs, then compare machine-verifiable structures against textbook arguments
• Articulate precisely where and why automated provers break down — and help map a path forward

Who You Are

• Advanced degree (Master's or PhD) in Mathematics, Logic, Theoretical Computer Science, or a closely related field
• Strong foundation in rigorous proof construction across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Hands-on experience with Lean (Lean 3 or Lean 4) — Lean 4 strongly preferred
• Experience with formal proof systems such as Coq, Isabelle/HOL, or Agda is a strong plus
• Deeply enthusiastic about formal verification, proof assistants, and mechanized mathematics
• Able to translate informal arguments into clean, structured, machine-verifiable proofs
• 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, data quality, or AI evaluation systems
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work on genuinely frontier problems — proofs that exceed the current capabilities of automated systems
• Collaborate with leading AI research labs on cutting-edge model training
• Gain direct exposure to how advanced LLMs are trained to reason mathematically
• Fully remote and asynchronous — work when and where it suits you
• Freelance autonomy with meaningful, intellectually stimulating work
• Potential for ongoing contract extension as new research projects launch