Lean 4 Proof Engineer - Mathematical Formalization
About this role
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
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