Data sets in chemistry and biology often arise from systems with strong geometric constraints: molecular configurations, rigidity conditions, distance relations, and shape spaces. These constraints frequently define real algebraic or semi-algebraic sets, making algebraic geometry a natural framework for studying the geometry of the underlying data. In this talk I will discuss how algebraic geometry can contribute to geometric data science by providing both models and computable invariants. I will focus on metric and topological questions: how densely must an algebraic set be sampled in order to recover its topology, and how can one design efficient sampling algorithms? Classical enumerative geometry and intersection theory enter naturally into these questions, connecting the geometry of algebraic varieties with effective computation and topological recovery. The talk is based on joint work with David Eklund, Oliver Gäfvert, Paul Breiding, Pierre Lairez, Jon Hauenstein, Martin Weinstein, and Peter Edwards.