"For the first philosophers... the unchanging principles of Nature were 'underlying substances' or ingredients. The vision they presented of all creation and annihilation as resulting from the expansion, contraction, and shuffling of unchanging material units... appealed more to imagination than to the intellect. ...So, alongside this idea of 'basic ingredients', the alternative idea grew up that mathematical axioms were the true principles of things. ...Explanations are arguments; so the bricks from which our ultimate explanations are built must not be objects, but propositions—not atoms but axioms. ...The most important result of this passion for rational demonstration was that, in addition to theoretical physics, the Greeks invented the whole idea of abstract mathematics. In Egypt and Mesopotamia, practical techniques of calculation had been highly developed... so one finds... the relationship between the sides of the right angled triangle measuring three, four, and five units; but the general theorem of Pythagoras is never stated, still less proved. Presenting mathematics as a system of general, abstract propositions, linked together by logic... [T]he most striking result of the Greeks' faith that the world could be understood in terms of rational principles was the invention of abstract mathematics."