Lean 4 Proof Engineer - Mathematical Formalization

Alignerr Corp.; Sheffield (TX); Remote; USD 83,000 - 165,000; Part time

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to translate informal mathematical arguments into machine-verifiable Lean formalizations for AI research. You’ll tackle proofs beyond current automation and contribute to the future of mechanized mathematics in a fully remote setting.

Ideal candidates hold a strong math background, proven proof-writing skills, and hands-on experience with Lean, Coq, or Isabelle/HOL.

Qualifications

• Master's degree or higher in Mathematics, Logic, or Theoretical Computer Science
• Strong foundation in rigorous proof writing across algebra, analysis, topology, logic, or discrete mathematics
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof assistants—Lean strongly preferred
• Deeply enthusiastic about formal verification and mechanized mathematics
• Able to translate dense informal arguments into precise formal proofs with minimal ambiguity
• Self-directed and comfortable working independently in an asynchronous, remote environment

Responsibilities

• Translate informal mathematical proofs into clean, structured Lean 4 formalizations with an emphasis on clarity, correctness, and reproducibility
• Analyze proofs across domains—identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants—especially where automation fails
• Investigate where automated provers break down and articulate the underlying reasons (complexity, missing lemmas, library gaps, etc.)
• Collaborate with AI researchers to design, refine, and evaluate formal verification strategies
• Provide expert guidance on proof decomposition, lemma selection, and structuring approaches
• Develop proof scripts that reveal deeper patterns or generalizations implicit in the original mathematics
• Compare machine-verifiable structures against classical textbook arguments to surface new insights

Skills

Mathematics

Formal verification

Proof writing

Independent work

Asynchronous work

Education

Master's degree

Tools

Lean 3

Lean 4

Coq

Isabelle/HOL

Agda

Job description

Lean 4 Proof Engineer — Mathematical Formalization (AI Training)

About The Role

What if your deep mathematical training could directly shape how AI reasons about formal proofs — and help push the boundaries of what machines can verify?

We're looking for mathematicians and formal verification experts to translate advanced mathematical arguments into precise, machine-verifiable Lean 4 proofs for cutting-edge AI research. You'll be working at the frontier — tackling proofs that lie beyond the reach of current automated tools, and helping define what the next generation of AI-powered mathematics looks like.

This is a fully remote, flexible contract role built for mathematically mature problem-solvers who love precision, structure, and the challenge of making the implicit explicit.

• 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 clarity, correctness, and reproducibility
• Analyze proofs across domains — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that test and extend the limits of existing proof assistants — especially where automation fails
• Investigate where automated provers break down and articulate the underlying reasons (complexity, missing lemmas, library gaps, etc.)
• Collaborate with AI researchers to design, refine, and evaluate formal verification strategies
• Provide expert guidance on proof decomposition, lemma selection, and structuring approaches
• Develop proof scripts that reveal deeper patterns or generalizations implicit in the original mathematics
• Compare machine-verifiable structures against classical textbook arguments to surface new insights

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 across areas such as algebra, analysis, topology, logic, or discrete mathematics
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable proof assistants — Lean strongly preferred
• Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal arguments into precise, structured formal proofs with minimal ambiguity
• Self-directed and comfortable working independently in an asynchronous, remote environment

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 pipelines
• Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies

Why Join Us

• Work directly with leading AI research labs on genuinely frontier problems in formal mathematics
• Fully remote and flexible — work on your own schedule, from anywhere in the world
• Freelance autonomy with meaningful, intellectually stimulating work
• Contribute to AI research that is actively shaping the future of mathematical reasoning and verification
• Potential for ongoing work and contract extension as new projects launch