When I was wee and being taught maths in the bad standard manner, I instinctively came up with little characterisations of various mathematical objects, to protect myself from boredom: The positive and negative numbers are mortally opposed armies; the modulus denotes the size of each army; each unit can handle one unit of the enemy before dying (evaporating together, in fact). Addition and subtraction are fair fights upon the field; multiplication and division are espionage and political overthrow. The negatives hate each other as much as they hate positives (-10 x -10 = 100). The positives are very simple and can be easily tricked into fighting for the other side (-1 x 1,000,000 = -1,000,000). Differentiation is desecration and zoom. Integration is reconsecration and overview. Going by the basic fairy-tale story arc , then, differdesecration is never the real end-point; a calculation isn't complete until it is brought back to the initial function... (Here we see the beginning o...