Is Math Art? Part II

Earth Day 2 (Aurora Australis and Bright Star Achernar)

When I started writing this post (several weeks ago!), I was aiming to answer the question posed in the title. I even thought I knew what I was going to say.

But — fortunately or unfortunately — these ideas are pretty complex. To write this post, I had to rethink my stance on some things I’ve said earlier in the semester. And that rethinking left me with even more questions.

Circle-style-warning

Warning: this post has many questions and few conclusive answers.

In the very first post on this blog, I asked,”Is math fiction?” In that discussion, I defined math as “the science of patterns.”

I’m not sure about that anymore.

Over the course of this year, I’ve written about math as a way to express relationships between things, as an exacting search for truth, and as a source of both cute puzzles and far-reaching ideas. In the post before last, I described my own deeply personal experience of math.

To my mind, “the science of patterns” is too vague to capture mathematics.

There is a sweet spot in the world of patterns that gives rise to good math. Good math is “interesting.” That term, “interesting,” gets thrown around by mathematicians a lot. It refers to a feeling people have about certain ideas and not other ideas, a feeling used to decide which patterns are worth studying.

Some “patterns,” like those of an argyle quilt, are too simple and lacking in meaning to be of interest to mathematics. Other logical structures are too complicated and discordant to be interesting. Not all patterns are math. And not all math is patterns.

Here is another possibility: because math is held to strict logical standards, one might try to define math as the study of logic. But math is more than pure logic. Just as important are guesswork, intuition, and creativity. If one is inclined to compare math to art, then logic could be called the medium of mathematics. It’s the paint, the charcoal, the clay, the language. If your image is not made from paint, it’s not a painting; if your idea is not logically consistent, it isn’t math. But the choice of what math to study — of which patterns to draw out, and which to leave be — is often a matter of taste. I don’t know any mathematician who feels he is grinding out dead logical statements.

I know mathematicians who study because they are curious about ideas, because they find them elegant or cute or perplexing and want to know more. A “nice” mathematical idea tugs at a person’s mind in a pleasant way.

All the diagonals of the elongated  pentagonal pyramid

I hope this blog has shown that side of math to people who didn’t know about it. Math is more than a tool to “feed big numbers into computers for some reason or other” (as Lockhart puts it). It is not just something people do to be smart or cryptic. It’s something people do because it’s fun, because they’re curious, and because it’s beautiful.

Personally, I think that joy is an amazing thing to be exposed to when you’re studying in a field.

Now, back to the original question.

Does that make math art?

Art is tricky to define. Perhaps Hardy, Lockhart, and others are simply using the term loosely. Or perhaps they see math in a way that I’m not advanced enough to see yet.

But I would say no. I don’t think math is art.

Still, I’m not done thinking about it. I haven’t really defined math, and I haven’t really defined art. This is only the beginning of a thought.

What do you think? What is math? Why do people do it? Is math art? Is “is math art” even a meaningful question?

Let me know what you think in the comments. Or ask something different. There are a lot more interesting questions to be asked, and we don’t have answers yet for most of them.

Isn’t that fun?

Earth Day 4 (Moon and Earth)