This post is about something I’ve been thinking about since my undergraduate days–the parallels between mathematics and the Imagist movement in poetry.
The key idea of Imagism was that a poem should describe its subject as it “truly is”, without unnecessary words, and without introducing the feelings and personal perspectives of the poet. In its unattainable ideal, an Imagist poem is poet-independent, in that one would hope that two Imagist poets writing about the same subject would write the same poem. And that poem would be the perfect poem on that subject, using exactly the right words in the most elegant possible way.
Perhaps the most famous Imagist poem is Ezra Pound’s “In a Station of the Metro.” Its two lines carry an incredible amount of meaning, and the word “apparition” all by itself seems to tell an entire story. If you’ve never read it, you should click on the link and do so. It will only take a few seconds.
“In a Station of the Metro” didn’t spontaneously appear to Pound in a flash of genius. He originally wrote a longer (30 line) poem. Six months later, he rewrote it, making it shorter. And it was yet another six months before he was able to refine his vision to its 14 word essence. Surely, the length of this poem betrays the amount of thought and energy that went into producing it.
I would argue that mathematics allows for writing that comes as close as possible to the Imagist ideal. The axiomatic approach makes it possible for different people to understand mathematical ideas in (almost) the same way, and the idea of perfect, maximally elegant poems corresponds to Paul Erdős’s idea that certain proofs are so perfect, they must be written in God’s own book of proofs.
When we teach, we want students to learn and appreciate these beautiful proofs. But we should emphasize that, like “In a Station of the Metro,” most of these proofs didn’t come easily, and the process was often similarly long and difficult. It may have taken years, even decades, for the grain of an idea to grow, ferment, and be distilled into an elegant proof.
Writing proofs can be hard, and students should know that it’s not supposed to be easy. Even when you understand in your mind why something is true, it’s sometimes hard to organize the steps neatly, linearly, and clearly. It’s necessary to write drafts, rewrite, edit, and revise. You shouldn’t expect to write an elegant proof in one sitting. Mathematics isn’t Beat poetry; it’s Imagism.