Critics of mathematics often call it “dry.” But if you ask me, they’re not going far enough. Mathematics is like Ben Stein reading an econ textbook in the Mojave desert: it exhibits several simultaneous kinds of dryness, and it’s worth unpacking what they are.
First, cultural dryness. Math often comes clothed in drab gray lectures and unmemorable texts. This is an artificial and undesirable dryness.
Second, technical dryness. Math is a highly technical discipline, and as such, tends to involve a certain level of fussy precision. Solving an equation is a kind of philosophical bookkeeping. That can be a little colorless, as careful bookkeeping is. This is a natural, neutral dryness.
Third, last, and most exciting (to me, anyway) is the dryness of abstraction.
As most practitioners of the subject will tell you, math has a Platonic purity. A simple equation or geometric form possesses an almost magical ability to refer to nothing in particular – and, thus, to everything.
In How Not to Be Wrong, Jordan Ellenberg describes math as a kind of x-ray vision. It allows you to see the conceptual skeleton of any situation, and thus to realize that totally different surfaces may disguise utterly similar structures. In my first book, I ape this insight with a metaphor of my own: mathematics is a series of Mario tubes, linking similar disparate quadrants of reality.
I think, when critics complain of math’s dryness, they mostly mean Dryness #1: the monotonous lessons of “open the book to page 127.” Sometimes, they mean Dryness #2: just as not everyone loves science or dance or U.S. history, not everyone loves the technicalities of math, and that’s okay.
But only on rare occasions do they mean Dryness #3.
This abstraction, I think, is a dryness to be celebrated and preserved. It’s a dryness that creates strange organisms – pricky pear cacti; desert pocket mice; topology – that could survive in no other climate. It’s the dryness that makes math “math.”