How did the shift from the times of Thales, Pythagoras, and even Euclid, where mathematical objects were found, exhibited, or constructed from given entities, to modern mathematics occur? In modern mathematics, entities no longer need to be constructed or computed in order to be named and manipulated; they simply need to exist. What was the transformative change that enabled this level of abstraction to be embraced and widely adopted, namely the distinction between mere existence and actual realization?