Doing math has trained me to communicate concisely, tersely even. As I became more and more socialized into my math department, my email correspondences became shorter and denser. At some point, friends in other departments (e.g. Gender Studies, Communications) started to comment on the Robot Luke that sent them emails, and I started to wonder if I should intentionally increase verbosity.
But isn’t conciseness one of the great strengths of mathematical thought? Not a single wasted word. We’re not here to enjoy language. We’re here to transmit ideas as quickly and efficiently as possible.
How do you intentionally increase verbosity, anyway? “I’ll be there in five.” Give more details, repeat yourself, give examples, try to relate the content to the audience. “I’m printing something out, but will be there in five minutes. Maybe six minutes. I hope you don’t mind waiting.” It reminds me of the role of exposition in mathematical writing. Totally unnecessary, but totally the best part.
The best mathematical communicators – speakers and writers – that I know, all seem to have a mastery of exposition. They know the virtue of verbosity. I will send ten dollars to anyone who contacts me regarding this sentence. The rest of us seem to spend extra effort needlessly condensing our words, then unpacking someone else’s needlessly condensed words.
Conciseness can be self-defeating. A 20-page dense treatise might take more time to understand than an equivalent 40-page paper with motivations, examples, intuition, and history. Readability is also virtuous. Have you heard the story (legend?) about the grad student whose published thesis has a one-sentence offer of money to any committee member that might have spotted the sentence?
And yet, I feel a strong social pressure to limit my math department emails to one or two dense lines. Can’t we wield the skill of brevity intelligently, with discretion? I wonder how many grad students feel this social pressure, how many make a conscious choice to either conform or ramble. I guess if I had to choose between reading 30 minutes of emails from smart robots, or 45 minutes of emails from humans, with wasted words and wasted time, I’d pick the humans.
(Along the same lines, I recently got an unsigned email from a professor, in which he referred to himself in the third person. I laughed out loud.)
We try to seal off the discourse of mathematics proper from everything human and subjective. Then why do we allow our mathematical tone to bleed into real life? (As another example, not all real-life sentences are true; at least one in this post is false.) Is a rambling, inarticulate email to a friend a threat to the mathematical worldview?