Lean 4 Proof Engineer - Mathematical Formalization

Alignerr Corp.; Seattle (WA); Remote; USD 83,000 - 165,000; Part time

Job summary

Alignerr is seeking a Lean 4 Proof Engineer to transform informal mathematical arguments into machine‑verifiable Lean formalizations. You will explore proofs across algebra, analysis, topology, and logic, identifying gaps and constructing robust formalizations that push the limits of current proof assistants.

You will collaborate with researchers to refine verification pipelines, ensure readability, and apply Lean idioms to complex mathematical problems.

Qualifications

• Master's degree or higher in Mathematics, Logic, or a closely related field.
• Strong foundation in rigorous proof writing across algebra, analysis, topology, logic, or discrete math.
• Hands-on experience with Lean (Lean 3 or Lean 4) and other proof assistants such as Coq, Isabelle/HOL, or Agda.

Responsibilities

• Translate informal mathematical proofs into Lean 4 formalizations.
• Analyze proofs across domains and identify gaps, assumptions, and formalizable sub-structures.
• Develop readable, reproducible Lean proofs aligned with best practices and Lean idioms.
• Collaborate with researchers to improve formal verification pipelines.

Job description

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.

This is a fully remote, flexible contract role. If you find beauty in precision, satisfaction in resolving gaps that automated tools cannot bridge, and excitement in working where mathematics meets machine intelligence, this role was built for you.

• 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
• Develop 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