Lean 4 Proof Engineer - Mathematical Formalization

Alignerr Corp.; Sheffield (TX); Remote; USD 83,000 - 193,000; Full time

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to translate advanced mathematical arguments into machine-checkable Lean proofs for AI training. This is a remote, flexible hourly contract designed for mathematically mature problem-solvers who value precision, structure, and explicit formalization.

You'll work with AI researchers to identify gaps, develop reusable proof scripts, and push the limits of current proof assistants.

Qualifications

• Master's degree or higher in Mathematics, Logic, or related field.
• Strong proof-writing and mathematical maturity across algebra, analysis, topology, logic.
• Hands-on experience with Lean 3 or Lean 4; Coq, Isabelle/HOL, or Agda preferred.

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

Proof theory

Lean proof writing

Formal verification

Mathematics

Proof analysis

Education

Master's degree or higher in Mathematics or closely related field

Tools

Lean (Lean 3/4)

Coq

Isabelle/HOL

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