Sylvester is an F# embedded DSL for mathematical computing that provides a single notation based on F# quotations for mathematical and logical concepts and expressions, which supports an integrated approach to computer algebra, theorem-proving, visualization, and other applications in computer-based mathematics. Sylvester provides a typed, functional-first, object-based language that captures conceptual, symbolic, logical, and visual properties of mathematical statements, together with a unified interface to tools like proof assistants, CAS, SMT solvers, and graph drawing libraries. This presentation describes the rationale and motivation of the Sylvester project, how Sylvester is implemented in F#, and how it can be used in different mathematical domains from set theory to linear algebra to real analysis.