[The Man]

I agree with most of that essay, but I must note that my experiences of both middle school geometry (7th grade, I think; I was really advanced) and high school calculus (10th grade) didn’t much resemble Lockhart’s descriptions of them. The approach I was taught in geometry focused on inductive rather than deductive reasoning: instead of deriving proofs by stringing together a bunch of abstract principles, we derived them by identifying patterns. It was almost certainly much more interesting as a result.

I don’t remember calculus nearly as well, but a good chunk of the class was definitely devoted to answering why things were done a certain way rather than simply having us memorise a number of formulas. We had to memorise those formulas, of course, since they were part of the BC Calculus test, but I’m almost certain we were given demonstrations of why they worked the way they did. I think Leibniz and Newton’s independent discoveries of calculus may even have been part of the curriculum.

I certainly agree with the central thesis of the essay that mathematics is a subject that can be an outlet for creativity, and that there is none of that left in the clinical, sterile approach that permeates most mathematics curricula these days. I’m not sure if we can completely strip out the arithmetic and various other rules from the curriculum without losing something, but they certainly shouldn’t be the exclusive or even primary focus of the pedagogy. I probably learned at least as much from just doing my own experiments with various principles we learned in class as I did from the homework.

And really, there are certain things no one is ever likely to use. Like probably almost everyone else in this country between ages 25 and 50, I don’t remember how to do long division, but I’ve only once as an adult been in a situation where it would’ve been at all helpful, and it still isn’t likely to have caused me any significant harm that I didn’t remember it.

One other flaw in the curriculum that this essay only addressed obliquely, but which certainly doesn’t afflict the essay itself, is that most textbooks are simply boring. This isn’t simply a flaw with mathematics textbooks; it’s a flaw throughout academia, particularly in STEM fields, and I don’t entirely know what can be done to fix it. I’m not even 100% sure what all the causes are, though I think the nature of the curricula probably contributes to some extent, as is the fact that many scholars are, to be frank, bad writers.

I almost feel everyone who publishes in academia should be legally required to re-read Orwell’s “Politics and the English Language” every five years or so; his advice isn’t flawless, but it’s unlikely that anyone who follows it will produce the bland writing that permeates not merely so much political science writing but so much academic writing of any strand. And to be honest, I noticed one case where Lockhart used “it’s” when he should’ve used “its”, but he’s still a much better writer than 95% of the textbook authors I’ve been subjected to over the course of my many years in school. I’ll give the textbook authors a slight amount of slack in that they have an almost insurmountable task in making their writing interesting, but there’s a bland tone that permeates so many textbooks that’s simply a recipe for zzzzzzz.