What’s missing in math? Witty, insightful quotes.
Mathematics has a problem.
Well, lots of problems, actually. (My favorite is the Kakeya Conjecture.) But I’m talking about a culture problem, a communication problem: the gap between mathematics as written and mathematics as practiced.
Mathematical work is full of loop-de-loops and dead ends. It’s multi-modal, multi-player, multi-dimensional, multicolored.
But mathematical writing is like a stone monument from a lost civilization. Opaque. Mystifying. Mathematical texts loom like obelisks in the desert, their meanings hard to trace, their origins almost impossible to imagine.
I propose a solution: the quotation.
Quotations have a mysterious dual property: highly contextual, yet utterly decontextualized.
A quotation, by nature, is a thing that someone said. It comes from a specific voice at a specific moment. That makes it personal, subjective. It has what mathematics often lacks: an actual human heartbeat.
Yet at the same time, a quotation becomes a quotation when it is lifted from that context. When you quote someone, you pass the microphone to someone who isn’t there, to say something that belongs to a different conversation. Decontextualization is what gives quotations their air of authority and universality–or at least, their quality of definiteness.
And so what better way than quotation to crystallize all the aspects of mathematics that are missing in our usual forms of discourse?
Which brings me to the context for these decontextualized thoughts.
A few days ago, at MathFest 2024 in Indianapolis, I ran a session titled Quotable Mathematics. Over a hundred mathematicians gathered in a ballroom; I pointed them towards a pile of pens and a stack of some 300 quotations; then I said, in so many words, “go to town.”
They voiced approval (
) and disapproval (X). They agreed and disagreed. They annotated and arranged. And, I hope, they assembled the raw material for speaking what has too long remained unspoken. I hope that they found quotations able to name and crystallize some of those unnamed vapors without which we’d be unable to breathe mathematics at all.
Some originally non-mathematical quotes (like this line, which I lifted from an Anna Sfard paper) found favor among the mathematicians:
Other witticisms incurred witty rejoinders of their own:
Sometimes a beloved speaker — like Bill Dunham, who just hours before had delivered a fabulous lecture on century-old Bryn Mawr entrance exams — drew surprisingly sharp disagreement. (Apparently we are over the 19th-century obsession with rigor, and have circled back around to intuition as foundational to mathematics.)
Some lines attracted silent nods of approval:
While others set off whole complex dialogues:
Not all the quotes went over as well as I imagined they would. One of historian Michael Barany’s favorite lines elicited raised eyebrows. (Perhaps we were not a crowd of pork-eaters.)
Meanwhile, an Edward Tufte favorite of mine, lifted from its original context on data visualization, no longer rang true.
On one table, the mathematicians arranged a pile of Rising Stars. Some happened to come from world-famous dead philosophers, but of course, the speakers are not the rising stars; it’s the words spoken.
One particular rising star was Nick Trefethen, a numerical analyst whose book of index-card musings I’d recently enjoyed, and from which I’d farmed a few favorite comments.
Some quotes stood out as particularly controversial–or not even controversial, just universally reviled, like Alfred Adler’s venomous assessments of mathematical research careers.
But the most fun we had was in arranging the great grid of wit and insight. With masking tape (borrowed from the fabulous Dave Richeson) I marked out two axes: wit on the x-axis, and insight on the y-axis. Then we arranged quotes in their appropriate positions, like a kind of real-world, real-time xkcd comic.
Here’s Dave attempting to document the results, while I settle for the easier task of documenting Dave’s documentation:
Unsurprisingly, a line from Terry Tao landed in the coveted top-right corner:
Although some folks felt that a similar sentiment had been even more felicitously expressed by Jordan Ellenberg:
I enjoyed the conversations arising from this line. (The point, I think, is that the incompleteness theorems mean that mechanistic processes can never encompass all of mathematical truth — so any mental process that can do so must be more than simply mechanistic.)
And even as this blog post stretches toward infinite length, I can barely do justice to the quotations and the commentaries. Here are a few more I saved from the recycling bin:
As the session hummed along toward its finish, many eager participants asked me things like “What’s your takeaway?” or “What are you hoping to achieve from this?” or “Do your actions on this planet ever have a purpose, Ben? Be honest.”
I told them the truth: I just wanted to see more fun quotations in circulation, and to accelerate the process of mathematical culture-building.
But I would like to extend this project beyond those delightful 90 minutes in Indianapolis. There are already some excellent compilations of mathematical quotations out there. I hope to create my own — ideally, a living and continually updated version, into which I and others can pour interesting quotes as we find them (with an eye toward greater diversity, in every sense of that word). If you’d like to join me as a partner in that project, reach out — I could use a co-creator with better Python skills (my own for loops being quite feeble).
Either way, I invite you to keep saying witty and insightful things, and — better yet — to quote such things when your colleagues say them. Speech fades; quotation is forever.