What can a small book for fiction writers offer to a mathematician? A lot, it seems. The Elements of Style, by William Strunk and E.B. White, is the most important book I’ve read this year, and reading it was an absolute joy. At just over 100 pages, it takes little time, but demands great attention. With watertight prose and unyielding attention to detail, the authors marshal the reader’s verbal reasoning into order. When I finished, my mind felt like a newly-neatened room.
Anyone who writes, or indeed speaks, will find the book useful. It explains how to construct phrases that are faithful to one's own thoughts, and that sympathise with the reader’s difficult task of interpretation. But the book is especially important for mathematicians, because it reveals how reason is most properly expressed: with order, completeness, and attention to detail. The book is mathematically beautiful, in that it both emphasises and demonstrates elegance and parsimony. It shows how constructing a sentence is like constructing a proof: there are many wrong ways to do it, a few right ways, and perhaps only one way to make it sing, where its structure reflects its content, and its construction places the emphasis in all the right places. The ‘singing' quality isn't the product of a gimmick; in fact, the discerning writer won't strive after it at all. Rather, it's accidental to the writing process, or rather, the cutting process. White tells the writer to chop away anything superfluous, leaving only a solid gem of composition. That is where style shines forth - not in the trappings, but in the substance. The author cannot help it.
This stripping-away is easier for the mathematician than for the prose writer, due to the different structures of their two languages. Mathematical expression is stingy by construction. It rarely admits the ornamental. As a result, when writing proofs, pure style often comes through. Still, mathematicians can get trapped by an over-emaphasis on formality. At best, this makes for a proof that’s boring to read, but at worst, it can impede reason. This is the second key virtue of White’s take on style: not only does good style aid the reader, but, if the voice on the page squares with the voice in one's head, writing becomes an act of open communication with oneself. That’s where creativity happens, where shoddy arguments are shown for what they are, and where strokes of brilliance can be captured, held, and processed in a way that wouldn’t be possible with unrecorded thought.
The final words of White’s introduction to Chapter 5 perfectly capture the interplay between the mind and the page:
"The mind travels faster than the pen; consequently, writing becomes a question of learning to make occasional wing shots, bringing down the bird of thought as it passes by. A writer is a gunner, sometimes waiting in the blind for something to come in, sometimes roaming the countryside hoping to scare something up. Like other gunners, the writer must cultivate patience, working many covers to bring down one partridge.”
Any mathematician knows just how fleeting a moment of inspiration can be. ‘The Elements of Style’ trains the writer, but more generally the thinker, how to refine his aim, to recognise a fleeting thought that ought to be timeless, and, by capturing it in the form that best reflects its content, to bring it to fulfilment.