The purpose of this essay is to contrast the definitions of what Plato and Nicomachus interpret Mathematics to be and the relationships within their respective texts. In Plato’s Republic Socrates describes various cities of different governments in great detail, he demonstrates how they came to be, and what principles lead to a certain government. After outlining the various types of government Plato mentions a “perfect number” (Republic. Bk VIII. 546b.) as well as the traits a leader or guardian of the city must have to govern, concepts that many of these governments lack. In the Nicomachus’ Introduction to Arithmetic, Nicomachus strongly agrees to the philosophy of Plato as he believes that with number can an individual be happy. While both…show more content… With this all the qualities of nature can be comprehended and related to an affection of the body in which they belong. And to understand these qualities of nature we must understand wisdom, “we crave for the goal that is worthy and fitting for man, namely happiness of life-and this is accomplished by philosophy alone and by nothing else, and philosophy, as I said, means for us desire for wisdom, and wisdom the science of the truth in things” (Nicomachus. Ch. II. Sec. 3). Nicomachus considered wisdom as the knowledge and understanding of this science, he mainly relates number as in an abstract realm. Abstract in the sense that number does not exist in a certain time or place it but rather an idea, “these studies [wisdom and number] are like ladders and bridges that carry our minds from things apprehended by sense and opinion to those comprehended by the mind and understanding” (Ch. III. Sec. 6). This can be directly related to the Divided line found in the passage of book VI in the Republic, and Nicomachus’ clearly agrees with this idea as well, with the arithmetic and other sciences training the mind’s eye to understand and decipher philosophy finally to Understanding. He then quotes Socrates agreeing that mathematical sciences are useful to the human life in that the mathematical sciences, “arithmetic for reckoning, distributions, contributions, exchanges, and partnerships, geometry for sieges, the founding of cities and sanctuaries, and the partition of land, music for festivals, entertainment, and the worship of the gods, and the doctrine of the spheres, or astronomy, for farming, navigation and other undertakings” ( Ch. III. Sec 7) are useful in improving the soul. From here Nicomachus begins with the importance of which mathematical science to
