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Imagine a world where kids are never exposed to the sound of music. Instead, they learn musical notation: how to read it, memorize it, and reproduce it. To these kids, notes, chords and songs are all just arrangements of dots on a page.

You would expect these kids to associate music with boredom and resentment. How else could they feel? They missed out on everything that makes music beautiful. They learned music as a written language, when really, music is a language in and of itself.

Fascinating? Not unless you can hear the music.

To a lesser extent, this happens to some people who feel that they don’t “get” math. In school, we learn mathematical notation, as well as how to get solutions to certain kinds of problems. But in this environment, many of us miss out on what makes math interesting.

Math is full of rhythms and harmonies that can only be perceived in the language of math itself. When someone says that e^(iπ)+1=0 is “beautiful,” they aren’t referring to the ink on the page or the pixels on their computer screen: they are referring to the beautiful pattern that those symbols represent. “e^(iπ)+1=0″ isn’t math. It is what you get when you translate math into written symbols.

Just as an expert composer can look at musical notation and hear the song in his head, a mathematician can look at written symbols and “hear the math” in her thoughts. The difference is that, while music can be performed on a piano or a bass guitar, there is no instrument on which math can truly be played. (The real medium for math is the human mind.)

Mathematical notation is a serious barrier for people who would otherwise enjoy math ideas. So in the Eye-Catching Math series, I will post and discuss beautiful mathematical images. This is a way to try to “play some math” without technical symbols. Images never fully capture how grand or astounding math can be, but they do a little.

The first post of this type will come out later this week. (The peacock and broccoli are actually examples of the first topic we’ll be discussing.) Enjoy!

The music analogy was inspired in part by Keith Devlin’s The Language of Mathematics.

Update, Nov. 30 2014: This post is accidentally similar to the introduction to Paul Lockhart’s A Mathematician’s Lament. No plagiarism intended! I hope to write about Lockhart’s lament in more detail in a future post.