Mathematical writing and Stained Glass

Photo of stained glass at Notre Dame by faraz_memon at flickr

This is an excerpt from an email reply to a student, who was asking about the form of answers to assigned questions. Great questions, keep 'em coming!

In keeping with mathematical culture, (for good or bad) assignment solutions are generally presented in a style that values economy of expression, elegance, and clarity over narrative, history, storytelling, individual experience, etc.

People sometimes make an analogy for this by talking about things like the huge stained glass windows in old cathedrals like Notre Dame in Paris. When you look at these, they are beautiful, airy, light, dazzling, glorious; you can see the beauty and grace and form that the designer intended us to see.

What you can't see is how on earth such a thing could have been built. If you are a builder of cathedrals, or have studied them, then you will know what went into it and be able to steal ideas, and admire the engineering genius, but as an outsider, you can only guess at the scaffolds, braces, ramps, pulleys, cranes etc. that must have been part of the process of transforming tonnes of rock, glass, and lead into a work of art.

It's the same with proofs, solutions, and lots of other kinds of communication - the author presents the only the final result, and leaves us to wonder and be inspired.