According to a study by sociologist Michael Handel, summarised here by Jordan Weissman, 75% of American workers never use any mathematics more complicated than fractions in their work. (It goes without saying that most partake of recreational calculus, at least on weekends…) Writing in the NY Times last year, Andrew Hacker argued that most schoolchildren are wasting their time learning mathematics: They’ll never understand it, and they won’t be any the worse off for it. As for scientists, the great entomologist E. O. Wilson has recently taken to the pages of the Wall Street Journal to argue that
exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory.
For that matter, even Albert Einstein famously remarked to a schoolgirl correspondent
Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.
But that was after he’d mostly decamped from physics for sagecraft.
Wilson goes on to portray mathematical biologists as technicians, armed with useful tools and useless ideas. And if you need them, you just hire them. (It’s not like they have anything important to do with their time.) So what’s going on? Are mathematicians scamming the public, teaching algebra and other unnecessaries to justify their existence? I would suggest that there are several important issues that these wise men are ignoring or underplaying:
- It may be true (as Hacker argues) that only a tiny techno-elite actually needs to know how a computer works, or how to compute the trajectory of a spacecraft, or how to program a Bayesian network. But when they’re 11 years old you don’t know who will have the interest or aptitude to join that elite. If you start sieving the children out early because they don’t seem like a likely candidate for that track — and let’s be honest, a lot of the tracking is going to be based on parental status and educational attainment — most of them will have no way to change tracks later on, because of the cumulative nature of mathematical understanding. Worth noting, in this context, is Handel’s observation (cited above) that skilled blue collar jobs are actually slightly more likely to require “advanced maths” (algebra and beyond) than skilled white collar jobs. So you can’t decide who needs the advanced maths based on the kinds of work they’re going into. Those without the education are simply more likely to be stuck at the lower rungs of whatever trade or profession they go into. (On the other hand, a larger fraction of white collar workers are in Handel’s “upper” (skilled) category, so an average blue collar worker probably needs less maths than an average white collar worker.)
- Mathematics is a language. And what is discussed in that language is, as Hacker recognises, crucial to the fate of everyone in the world. Those who have not learned at least the rudiments of the language are excluded from the conversation. I am reminded of a friend who dismissed the value of learning to speak French, with the argument that “Everyone in France speaks English.” Now, France might have been a bad choice for his claim, but even if it were true, it puts you at a significant disadvantage to be surrounded by people who speak your language, while you can’t decipher their language to understand what it is they’re saying to each other.
- Think about that Einstein quote: Everyone finds mathematics difficult when they’re pushing beyond their current knowledge. If we’re going to drop mathematics training when it becomes challenging, we might as well stop counting when we run out of fingers and toesies.
- I would suggest that Wilson may be using more sophisticated mathematics in his work than he is aware. To paraphrase J M Keynes, practical biologists who believe their work to be quite exempt from any need for mathematics, are usually the slaves of some defunct mathematician. Modern biologists of bench and field are often quite attached to some mathematical and statistical machinery that happens to be some years old, and seemed impossibly abstruse when it first seeped in from the pure mathematics or theoretical statistics world. Many of the attempts to apply mathematical techniques in biology (or sociology or economics or whatever) will prove more clever than enlightening, but some will stick, and become part of the basic toolkit that the biologists who think they don’t need any sophisticated math do use. Wilson’s arrogant posture really reflects the fact that there are far more trained mathematicians who are intellectually flexible enough to try and figure out what the biologists are doing, and what the connections might be to their own field, than trained biologists willing to work in the other direction.