Mathematician, Foundation Team

Why "Hilbert" The company takes its name from Hilbert's program. A century ago, mathematics went through its foundational crisis: paradoxes in set theory had undermined confidence in the ground the discipline stood on. David Hilbert's response was to rebuild it on explicit axioms and formal proof, so every claim could be traced back to its foundations. Gödel later showed the program's full ambition was out of reach. Any sufficiently rich formal system contains true statements it cannot prove. The program still reshaped mathematics; proof theory, model theory, and modern logic all descend from it. We think growth is at a similar moment. The field runs on intuition, folklore, and case studies. We are building its foundations: definitions, axioms, and proofs where proofs exist. We expect incompleteness. Some true statements about growth will remain unprovable, and that is fine. No Gödel is expected to destroy anything here, because completeness was never the claim. The claim is that far more of growth can be formalized than anyone has attempted, and that the formal core is worth building. About Hilbert Hilbert is an a16z-backed, AI-native growth intelligence platform for consumer companies. We work with some of the largest retailers and consumer brands in the world, helping them understand and act on customer behavior at massive scale. We believe growth has formal structure worth writing down. Parts of it are repeatable and provable; parts of it will always resist proof. The Foundation Team exists to formalize the first kind and to know precisely where the boundary sits. You will: Work directly with the CEO and Chief of Staff on designing and building Hilbert's foundational system, from axioms up Formalize growth concepts using set theory and mathematical logic, and prove what can be proven Map what resists formalization, and keep the boundary between the provable and the empirical explicit Apply the formal system to active customer use cases, expanding its coverage with every engagement Coordinate closely with product, engineering, and data science teams to make the formal system usable in the product Become the go-to expert on Hilbert's logic and foundation system, knowing it inside out What We Are Looking For New graduate or entry-level, mathematician; no prior industry experience required Undergraduate-level (or deeper) knowledge of set theory, mathematical logic, and mathematical foundations. A background specifically in set theory is preferred Eager to learn, genuinely passionate about mathematics and foundational problems High energy and open-minded toward business questions Ready to rethink how businesses approach growth problems at the most fundamental level Ability to write clean, precise mathematical exposition What You Will Get A rare position: doing foundational mathematics inside a fast-moving AI company, with real datasets, real customers, and real stakes Direct daily exposure to the CEO and leadership A founding seat on a new internal team, with room to shape its direction Competitive compensation and equity How to Apply Send your resume along with a short note about the mathematical work you are most proud of: a thesis, a proof, a problem you could not let go of. We read every application.