By the Renaissance, mathematics was wide spread in all parts of life, including art, where the development of the golden section played a strong role in painting at the time. The historical peak of mathematics was the development of calculus by Newton as the basis for his theory of mechanics and gravitation. Calculus was so successful that the early numerological image of the Universe was replaced with a clockwork image. This clockwork model of the Universe reached its most developed form under Laplace in the late eighteenth century, who envisaged every atom in the Universe as a component in a precise cosmic mechanism. Infinity, in Western culture, means endless or immeasurable.
Infinity commonly inspires feelings of awe, futility and fear.
Thus, apeiron means not only infinitely large, but infinitely complex. Plato rejected the concept of infinite following the tenets of Pythagoras that any given aspect of the Universe could be represented by a finite arrangement of natural numbers. Aristotle recognized that there are many aspects of the Universe that point to the actuality of the apeiron. However, to protect his a priori finite world, Aristotle invented the notion of potentially infinite as opposed to actually infinite. For example, Aristotle would state that the set of natural numbers is potentially infinite, since there is no largest natural number, but he would deny that the set is actually infinite, since it does not exist as one finished thing.