Last week Michael J. Barany — a mathematical historian — published a blog post in Scientific American titled Mathematicians Are Overselling the Idea That “Math Is Everywhere.” We can talk about whether or not the main arguments of his article have merit in a moment, but first, let’s start by dismissing the title as little more than an editorial blunder. It gives the impression that Barany intends to argue that math actually isn’t everywhere, despite what all those mathematically enthusiastic look-around-you-math-is-hidden-in-the-fabric-of-our-lives media types would have you believe.
This is not the point of Barany’s post at all, in fact it’s barely even mentioned beyond the title and a passing
dig at mention of Jordan Ellenberg. Instead, what it seems Barany is endeavoring to establish is that mathematicians are not everywhere. And this, he says, should be considered when making policy decisions concerning public support of advanced mathematics.
Barany discusses the role of mathematics in society and culture from the Babylonian times through post-World War II.The ancients, he says used math as “a trick of the trade rather than a public good,” adding, “for millennia, advanced math remained the concern of the well-off, as either a philosophical pastime or a means to assert special authority.” Historically, Barany explains, math was the domain of the elite, it was a source of power that was only available to the highest born. Mathematicians inhabited a rarefied domain, they were acting as advisors to heads of state and maintained an untouchable air of the occult.
This otherness and elite status meant that math wasn’t available to all people, and Barany argues that this has bled through to mathematics today. And I completely agree. Anecdotally — since I can’t find an actual demographics survey to back this up — advanced math is largely occupied by people who come from the economically advantaged side of things. But here’s where Barany’s argument starts to lose some strength: isn’t that the case for any course of advanced study? Attending graduate school at all is a tremendous luxury, whether studying math, science, language, or art, it’s a pretty brazen thing to want to sit around for 4-6 years to get paid very little to think about things.
And some historians, most notably the blogger Thony Christie, even take exception with the picture Barany paints of math and society. Christie suggests that Barany may her oversold the elitism and “otherness” of mathematicians, pointing out that math played a huge role in the scientific revolution of the seventeenth century. Confirming what I suspect, which is that math isn’t all that different from the other sciences in terms of its growth and expansion over the last several centuries.
In a conversation on twitter, Barany defends his position to Steven Strogatz — legendary bringer of math to the people — saying there are two core questions that people try to answer with “math is everywhere” namely, (1) why should the public support advanced math, and (2) why should the public learn basic math? Barney contends that “math is everywhere” is not an appropriate answer to either. I disagree.
I think math being everywhere is exactly the antidote to the ancient rhetoric of “when will I ever use this?” Math is everywhere just as much as anything is everywhere. Science is everywhere, art is everywhere, language is everywhere, and for some reason in those cases, being everywhere is sufficient to convince folks that they will use the subjects. It is everywhere, and therefore knowing it will help you understand everything. So I think a good dose of “math is everywhere” is a great way to motivate why the public should learn basic math. And I think we can mostly agree that learning basic math is a good and important thing.
And since the best way to help your kids develop good habits is to set a positive example, I obviously think policymakers should opt in favor of supporting advanced math, just as they would support any advanced science research. Because even though it often seems pointless, basic research is the provenance of great discovery.
“Math is everywhere just as much as anything is everywhere. Science is everywhere, art is everywhere, language is everywhere, and for some reason in those cases, being everywhere is sufficient to convince folks that they will use the subjects. It is everywhere, and therefore knowing it will help you understand everything.”
The above lines strike me as a reductio ad absurdum in favor of Barany’s point, not a contradiction to it.
1. The ubiquity of art does not convince folks they will use the subject; ditto language (arts). Enrollment in humanities programs (at the university level) has been proportionally shrinking for decades as has robust humanities offerings in K-12 education. Federal research $$ prioritize humanities << general science < medical science < 1, then those things cannot all be simultaneously salient. By making the claim that “math is everywhere”, we get called on defend its importance in situations where it is at best a secondary or tertiary factor. While an election may have mathematical aspects, psychology and politics seem much more important to me. So too with love (pace Frenkel) and farming. Situations where math is more fundamental than incidental are many but also rare (like, small % large #). The phenomena in which it is fundamental are often also very abstract or technically difficult, so a popular book like Ellenberg’s reads like a kind of cabinet of curiosities. Game-able lotteries are interesting, make for fun reading, but not important. Stability analyses for bridges and skyscrapers are interesting, make for more difficult reading, and are very important. I would prefer to defend the claim that the salience of math is distributed quite unevenly across human activity and interest, that where it is most salient it is essential, the difference between life and death, tied up in the origins of the universe and the nature of matter. The pleasure of mathematics is not its ubiquity but its quality.
[Here I mean mathematics beyond algebra. Basic numeracy is pretty darn helpful for making decisions in the world, and policy-makers and the public agree on the importance of arithmetic.)
3. Bacteria are more everywhere than language, but that doesn’t mean we should prioritize the study of bacteria over literacy. Ubiquity does not establish priority.
I’m somewhat surprised to find myself making a late-night comment on your blog, but it just happened! Thanks for writing, Anna.
Please stop referring to mathematics as science. It is not in any sense a science.