Is Beauty Truth?—Part 1

For a couple of centuries scientists, mathematicians, and philosophers have argued about the validity of the last two lines of John Keats Ode on a Grecian Urn: “Beauty is truth, truth beauty—that is all/ Ye know on earth, and all ye need to know.” Keats seems to be equating truth and beauty in these lines, and there are many who agree with him. However, there is an equally adamant group of folks who take issue with Keats and find all sorts of reasons why beauty and truth are not the same, or at least that one does not necessarily imply the other.

As often happens when parties disagree, they frequently are using different definitions, and there are few words that have more contradictory interpretations than beauty and truth. Beauty certainly is a relative term—one person’s beauty is another’s ugly. Truth, although it infers an absolute state, can at best be only partially fathomed by us humans. Truth, if we pursue it unwaveringly, may slowly reveal itself, but we can never fully own it. So the arguments persist. If people can’t even agree on whether something is true or not, or whether it’s beautiful or not, how do they ever expect to settle the dispute of whether or not they are equivalent?

I recently read a book by the eminent British mathematician and prolific writer Ian Stewart, that unequivocally takes a stand on the issue. Stewart titled his book Why Beauty is Truth. It’s really “a history of symmetry” (that’s the subtitle of his book), but along the way he builds a pretty strong case for why “beauty must be true,” but he does so in a rather narrow definition of each term.

One of my frustrations in reading the book (besides having my brain become numb by all the pure mathematics he goes into) is that Stewart never clearly defines what he means by either beauty or truth. He seems to assume that anyone brash enough to tackle his book will already know what truth and beauty are, as he uses them. He’s kind of like the musician who delves into a detailed lecture on timbre and counterpoint rhythms, assured that everyone is familiar with those words.

The book was still rewarding for me to tough out, though. Afterwards I kept pondering what beauty and truth are, as Stewart uses them. Here’s what I came up with, thanks one more time to wonderful Internet resources. (I really appreciate Wikipedia!)

Stewart—being a mathematician—is primarily concerned with mathematical beauty. Pure mathematicians love to refer to a mathematical concept or proof as beautiful, and when they do they usually mean that it is elegant, in the sense of being (1) clean, with a minimum of details, (2) succinct, and/or (3) original and unexpected (as in a discovery of some fundamental mathematical relationship). In other words, it must be simple, straightforward, unique, and balanced.

When a mathematician plays with theoretical concepts in algebra, geometry, and number theory, and eventually comes upon a pure, simple insight, he literally gets a feeling of aesthetic pleasure and considers it beautiful. The Babylonian and Greek mathematicians fell in love with the beauty they found (particularly Pythagoras’s geometrical discoveries).

Next time, truth…