Thomas Mann once said, “A writer is someone for whom writing is more difficult than it is for other people.”
I believe the same applies to mathematicians doing arithmetic.
It’s a running joke among mathematicians that they’re bad with numbers. This confuses outsiders, like hearing surgeons plead clumsiness, or poets claim illiteracy, or Rick Astley confess that actually he is going to give you up and let you down, maybe even run around and desert you.
Does it come from some false modesty? A skewed sense of humor?
No, some mathematicians insist: it’s really true, we’re bad at arithmetic.
I’m choosing my words carefully: “mathematics” and “arithmetic” are not interchangeable. “Arithmetic” refers to calculations with numbers: 17.9 + 18.32, for example. “Mathematics,” meanwhile, is far broader: it tackles shape, structure, change, and all kinds of quantities.
The reality is that mathematicians aren’t professional arithmetic-doers, any more than musicians are professional players of scales.
I’ve heard mathematicians lament that their ability with arithmetic peaked sometime in grade school. That sounds overblown, but they’re probably not wrong.
As early as high school, specific numbers start taking a back seat to patterns among numbers. You stop working with 7 and 9 and 22, and start working with an x or an n that can refer to all of them at once. As you move into more abstract realms, your arithmetic gets rusty.
And the more math you study, the more extreme this gets.
When I began to teach 3D vectors two years ago, I realized I first had to teach it to myself, because I’d never actually learned it. My college courses skipped straight to “n-dimensional vectors.”
This is how mathematicians approach things: why discuss the 2D or 3D case when you can just climb the ladder of abstraction and cover all cases at once? Surely you can figure out the 3D specifics when you need them, right?
But going from abstract to concrete isn’t always as easy as you’d think.
I’m not a professional mathematician, but I’m proud to say I have all the bad habits of one. To wit: my students are often surprised at my clumsiness with arithmetic. Just today I casually said “40,000” when I meant “400,000.”
This happens a lot.
Now, are mathematicians actually that bad at arithmetic? Compared to engineers and accountants, perhaps. Compared to the average person on the street, of course not. The “bad at arithmetic” thing is probably overplayed. So why do mathematicians love to bring it up? Here’s one reply:
Imagine you’re an artist, and people are convinced that your job consists of rolling and unrolling canvasses. That’s it.
Week after week, people ask: How fast you can roll a canvas? What’s the biggest canvas you’ve ever unrolled? Can you come over and unroll my canvas for me this weekend? And so on, and so on.
You keep trying to clarify – to talk about the actual paint you put on the canvas – but they don’t really get it. They just laugh and say, “Oh, you artists!”
Wouldn’t you start pretending to be bad at canvas-rolling, just to change the subject?
That’s one answer. But I have to admit there’s another possibility: