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

Why join us

At Hilbert, we move fast, work collaboratively, and give people real ownership over their impact. As a fast-growing company, there's no shortage of room to grow — you'll take on new challenges quickly and shape the path as you go.

On top of that, here's how we take care of our team:

Health & wellness. We cover 100% of your Health, Dental, and Vision premiums — with the option to add coverage for dependents or a spouse at additional cost.

Financial future. Plan ahead with our 401k through Human Interest, including an employer match that vests immediately.

Time to recharge. Enjoy generous PTO so you can rest, travel, and spend time on what matters most outside of work.

Commuter support. Based in SF? We help cover your commuting costs.

Lunch, covered. In the SF office, we provide lunch vouchers via DoorDash.

And many more. We're always looking for new ways to support our team. Come build the future with us, and grow alongside a company that's investing in yours.

Hilbert is an Equal Opportunity Employer. We are committed to building a diverse team and an inclusive culture, and we welcome applicants of all backgrounds. All qualified applicants will receive consideration for employment without regard to race, color, religion, sex, gender identity or expression, sexual orientation, national origin, age, disability, veteran status, or any other status protected by applicable law.