Throughout the history of science, computational, mathematical and statistical breakthroughs were needed to address questions at the core of the human experience. In the decades to come, as the nature of data becomes ever more complex, the new fundamental advancements will arise out of a collaboration across the three disciplines - computer science, mathematics, and statistics. These advancements will call researchers and educators in each of these three disciplines to learn from each other and work together, developing new mathematical, statistical, and algorithmic principles which will strengthen the foundations of theoretical data science while driving discovery and innovation for emerging applications. The vision of UA TRIPODS is to provide the infrastructure and environment so that data scientists at the foundations will become vital partners on the journey to the new frontiers of knowledge. At the same time, UA TRIPODS aims to help establish and encourage a diverse population to pursue careers in quantitative and computational data science by offering a broad spectrum of research, education and outreach programs tailored to high school students through post-doctoral fellows.