Mathematical Formalization Specialist
About this role
About the Role What if your deep mathematical training could directly shape the future of AI reasoning? We're looking for mathematicians with hands-on experience in formal proof systems — particularly Lean — to work on some of the most intellectually demanding problems in AI development today. This is a fully remote, flexible contract role working alongside leading AI research labs. You'll be translating rigorous human-written mathematics into machine-verifiable formal proofs, operating at the very edge of what proof assistants can currently express and automate. - Organization: Alignerr - Type: Hourly Contract - Location: Remote - Commitment: Flexible What You'll Do - Translate informal mathematical proofs into Lean (and related proof systems) with precision, clarity, and structural rigor - Analyze domain-specific proofs to identify gaps, hidden assumptions, and formalizable sub-structures - Construct formalizations that probe the limits of existing proof assistants — especially where automation fails - Collaborate with researchers to design, refine, and evaluate strategies for improving formal verification pipelines - Develop readable, reproducible proof scripts aligned with mathematical best practices and proof assistant idioms - Provide expert guidance on proof decomposition, lemma selection, and formal modeling strategies - Investigate and articulate the reasons automated provers break down — whether due to complexity, missing lemmas, or library gaps Who You Are Must-Have: - 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 a comparable formal proof system — Lean strongly preferred - Deep enthusiasm for formal verification, proof assistants, and the mechanization of mathematics - Ability to translate dense, informal arguments into clean, structured, machine-verifiable proofs 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 - Strong communication skills for articulating formalization decisions, edge cases, and reasoning strategies Sample Work You Might Do - Formalize classical proofs and compare machine-verifiable structures against textbook arguments - Investigate where automated provers break down and document the underlying causes - Create Lean proofs that surface deeper patterns or generalizations implicit in the original mathematics - Help map the frontier of what formal verification can express, capture, and eventually automate Why Join Us - Work on cutting-edge AI research projects alongside leading labs pushing the limits of machine reasoning - Fully remote and flexible — work on your own schedule, from anywhere - Freelance autonomy with the depth and challenge of genuinely frontier-level mathematical work - Contribute to a field that is reshaping the reliability and rigor of AI at its core - Potential for ongoing work and contract extension as new projects launch
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