"Some philosophers have reached the startling conclusion that Truth is made by men, and that Mathematics is created by mathematicians and that Columbus created America: but common sense, it is refreshing to think, is at any rate above being flattered by philosophical persuasion..."
― Philip E.B. Jourdain, The Nature of Mathematics
Have you ever considered the power of definition? As a mathematician I can define "x" to be an integer or "A" to be a set of numbers. These are mathematical objects which inhabit the sentient mind and come into existence only by definition. Now these objects may correlate to objects in reality like the mathematical object called a circle corresponds to the rough approximation to said circle that I can draw on paper. But these objects do not exist in any physical sense. There is no integer, set, or circle that I can discover in the physical world and study to determine it's properties. So are these mathematical objects simply a product of the sentient mind or do they have some kind of independent existence?
