Lean Proof Engineer - Mathematical Formalization

Position: Lean 4 Proof Engineer - Mathematical Formalization
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 classic 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