The article "50 years of Data Science" by the David Donoho has been influential in characterizing the workflow of Data Science research. It also outlines the recent history of Data Science from the perspective of the interplay between computer science and statistics. The focus of this talk will be on geometry and the applications of geometric frameworks to Data Science and how these ideas provide insight into understanding fundamental tools such as dimension reducing mappings. We start with optimal linear transformations which we trace to Beltrami and Jordan. We proceed to nonlinear data reducing mappings which are rooted in artificial neural networks. We will include at least 5 intriguing applications of the singular value decomposition and advocate that mathematical theory, e.g., Whitney's theorem, plays a central role in the Foundations of Data Science.