What have been some of the most revolutionary philosophical shifts in perspective in mathematics? Often times, great revolutions in mathematics come from shifts in philosophical perspective. The shift from extrinsic to intrinsic geometry yields manifolds (and much else). The shift in focus from objects to the maps between them is the shift from set theory to category theory. What other shifts in perspective have there been which have led to great advances and revolutions throughout mathematics? I apologize if this question is vague.

The Greek shift from the applied mathematics required e.g. to build pyramids to an axiomatic approach as personified by Euclid deserves mention.
