Lean 4 Proof Engineer — Mathematical Formalization

About The Role

What if your deep mathematical training could directly shape the future of AI — by pushing the boundaries of what machines can understand, verify, and reason about?

We're looking for mathematicians and formal verification specialists to translate rigorous mathematical arguments into machine-verifiable Lean 4 proofs for cutting-edge AI research. This role sits at the frontier of mathematics and computer science, where human intuition meets the precision of formal proof systems.

This is a fully remote, flexible contract role — ideal for someone who finds genuine satisfaction in the challenge of expressing elegant mathematical arguments in a form a machine can verify.

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 Work at the frontier of formal verification, constructing proofs that test or exceed the current capabilities of automated provers Investigate where automated provers break down and articulate why — missing lemmas, complexity limits, insufficient libraries Collaborate with researchers to design and refine strategies for improving formal verification pipelines Guide proof decomposition, lemma selection, and structuring techniques for formal models Formalize classical proofs and compare machine-verifiable structures against textbook arguments Develop Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics

Who You Are

Hold a 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 4 strongly preferred Able to translate dense informal arguments into clean, structured formal proofs Deeply enthusiastic about formal verification, proof assistants, and the future of mechanized mathematics

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 workflows Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies

Why Join Us

Work on genuinely frontier problems at the intersection of mathematics and AI Collaborate with world-leading AI research teams and labs Fully remote and flexible — work when and where it suits you Freelance autonomy with the structure and intellectual depth of meaningful research-adjacent work Gain exposure to how advanced AI models are trained and evaluated Potential for ongoing work and contract extension as projects evolve