Lean 4 Proof Engineer — Mathematical Formalization (AI Training)
About The Role
What if your deep mathematical expertise could directly influence how the world's most advanced AI systems reason, prove, and think? We're looking for Lean 4 Proof Engineers to translate rigorous human mathematics into machine‑verifiable formalizations — working at the precise frontier where formal verification meets cutting‑edge AI research.
This is a fully remote, flexible contract role built for mathematicians who find beauty in precision and satisfaction in expressing dense, elegant arguments in a form a machine can verify and learn from.
Organization: Alignerr
Type: Hourly Contract
Location: Remote
Commitment: 10–40 hours/week
What You'll Do
Translate informal mathematical proofs into Lean 4 — emphasizing clarity, correctness, and structural elegance.
Analyze proofs across domains, identifying hidden assumptions, logical gaps, and formalizable substructures.
Construct formalizations that push proof assistants to their limits — especially where automated tools struggle or fail entirely.
Collaborate with AI researchers to design and refine formal verification strategies and pipelines.
Develop highly readable, reproducible proof scripts aligned with mathematical best practices and Lean idioms.
Provide expert guidance on proof decomposition, lemma selection, and structuring techniques for formal models.
Formalize classical and advanced proofs, then compare machine‑verifiable structures against textbook arguments.
Articulate precisely where and why automated provers break down — and help map a path forward.
Who You Are
Advanced degree (Master's or PhD) in Mathematics, Logic, Theoretical Computer Science, or a closely related field.
Strong foundation in rigorous proof construction across areas such as algebra, analysis, topology, logic, or discrete mathematics.
Hands‑on experience with Lean (Lean 3 or Lean 4) — Lean 4 strongly preferred.
Experience with formal proof systems such as Coq, Isabelle/HOL, or Agda is a strong plus.
Deeply enthusiastic about formal verification, proof assistants, and mechanized mathematics.
Able to translate informal arguments into clean, structured, machine‑verifiable proofs.
Self‑directed and comfortable working independently on complex, open‑ended problems.
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, data quality, or AI evaluation systems.
Strong communication skills for explaining formalization decisions, edge cases, and reasoning strategies.
Why Join Us
Work on genuinely frontier problems — proofs that exceed the current capabilities of automated systems.
Collaborate with leading AI research labs on cutting‑edge model training.
Gain direct exposure to how advanced LLMs are trained to reason mathematically.
Fully remote and asynchronous — work when and where it suits you.
Freelance autonomy with meaningful, intellectually stimulating work.
Potential for ongoing contract extension as new research projects launch.
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