Lean 4 Proof Engineer - Mathematical Formalization

About the Role

What if your deep mathematical training could directly shape how AI reasons about formal proof — helping machines understand arguments that push the very limits of what automated systems can verify?

We're looking for mathematicians with serious proof-writing credentials and hands-on experience with formal proof assistants — especially Lean 4 — to work at the frontier of mathematical formalization for cutting-edge AI research.

Organization

Alignerr

Type

Hourly Contract

Location

Remote

Commitment

10–40 hours/week

What You'll Do

• Translate informal, human-written mathematical proofs into rigorous, machine-verifiable Lean 4 formalizations
• Analyze proofs across domains — algebra, analysis, topology, logic, discrete mathematics — identifying gaps, hidden assumptions, and formalizable sub-structures
• Construct formalizations that actively test the limits of existing proof assistants, especially where automation fails or falls short
• Investigate why automated provers break down and articulate the underlying causes — missing lemmas, library gaps, complexity barriers, and more
• Create clean, readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms
• Collaborate with researchers to design and refine strategies for improving formal verification pipelines
• Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models
• Create Lean proofs that expose deeper patterns or generalizations implicit in the original mathematics

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 one or more areas: algebra, analysis, topology, logic, or discrete math
• Hands-on experience with Lean (Lean 3 or Lean 4), Coq, Isabelle/HOL, Agda, or comparable formal systems — Lean 4 strongly preferred
• Deep enthusiasm for formal verification, proof assistants, and the future of mechanized mathematics
• Able to translate dense, informal arguments into clean, 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 where automated reasoning frequently fails or requires manual scaffolding
• Prior involvement in data annotation, quality evaluation, or AI training workflows
• Strong communication skills for explaining formalization decisions, edge cases, and proof strategies to non-specialists

Why Join Us

• Work directly with leading AI research labs on some of the most intellectually challenging problems in formal mathematics
• Fully remote and flexible — work when and where it suits you
• Freelance autonomy: set your own pace, own your process, and collaborate globally
• Contribute to work that sits at the frontier of what machines can understand and verify
• Potential for ongoing work and contract extension as new projects launch