Universes as big data

We briefly overview how, historically, string theory led theoretical physics first to precise problems in algebraic and differential geometry, and thence to computational geometry in the last decade or so, and now, in the last few years, to data science. Using the Calabi-Yau landscape -- accumulated by the collaboration of physicists, mathematicians and computer scientists over the last 4 decades -- as a starting-point and concrete playground, we review some recent progress in machine-learning applied to the sifting through of possible universes from compactification, as well as wider problems in geometrical engineering of quantum field theories. In parallel, we discuss the programme in machine-learning mathematical structures and address the tantalizing question of how it helps doing mathematics, ranging from mathematical physics, to geometry, to representation theory, to combinatorics, and to number theory.