The Origin of Mathematics 11: Math Is Beautiful

When mathematicians praise the aesthetic qualities of their subject, they usually meet raised eyebrows from sceptical nonbelievers. What will be said here will probably not convince outsiders, but it may clarify the situation somewhat for ourselves. Using examples as well as comments by some prominent authors, we will try to be more specific than just stating an emotional opinion. Proclus will again be our main witness from antiquity. He discusses the applications of mathematics and then goes on to describe its superior beauty and its value for the study of philosophy. In part he elaborates a short passage from Aristotle, who says what beauty is: “The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree” (Aristotle, Metaphysics 1078 a34-b2). (Here, as in the quotation from Proclus below and in many other places, the translator has used the modern “symmetry” for the Greek “symmetria “ which, at least in a mathematical context and by its literal translation, should mean “of common measure.” In most cases the literal translation makes much more sense than the modern word “symmetry,” which has taken on quite a different meaning outside of mathematics.)