Who needs algebra? Mathematicians!

Who Needs Algebra? (NY Times, possibly behind paywall)

I have a feeling of deja vu here, since 5 or 10 years I wrote a blog-response to an editorial by Roger Schank that called (roughly) for the elimination of certain math classes from high schools. Schank’s argument was roughly the same as this one – you don’t need math for most jobs, or most life situations, so whoneedzit?

I’ll tell you who needs mathematics: mathematicians. (I am not kidding.) Also, of course, people in closely allied fields: physicists, engineers, actuaries, statisticians etc.  But for rhetorical effect, let’s stick with mathematics.

If someone is going to become an algebraist, they will first have to “struggle with algebra” (in the sense of solving-for-x and factoring polynomials), and then they’ll have to “struggle with algebra” (in the sense of re-proving certain well-known elementary theorems about groups and fields) and then if they are lucky they will qualify to “struggle with algebra” (in the sense of helping humankind to figure out under which conditions the free universal algebra of an uncountable signature over a metrizable space is paracompact (yeah, I looked that one up) – in other words, do original research in mathematics).

The main point here is that mathematical disciplines are a strenuous and cumulative track and, to a first approximation, once you’re off the track you’re off the track for good. (I can tell you when I got off the track: later than many but still quite early, at age 22, after a particularly cruel course in point-set topology.)

I suspect that there are no Olympic medal-winners in gymnastics who did no gymnastics between ages 10 and 16.  Similarly, I bet that there’s no one on the mathematics faculty of a good university (let alone Nobel and Fields medal winners) who did no mathematics between ages 10 and 16. If as a country we decided that there would be no gymnastic classes, starting right now, I think we would give up our Olympic dreams in gymnastics in 2020. We should expect a similar result in math and science if we eliminate “onerous” math classes country-wide.

Now the anti-math-class argument potentially divides into two alternatives:

1) No one needs math (not even mathematicians, physicists, statisticians, because we don’t need them).

2) Most people don’t need math, because, y’know, most people aren’t going to be mathematicians, scientists, or engineers.

I won’t even bother to reply to #1. As for #2 – that is true, but can you pre-identify those people before they start “struggling with algebra”? And do we want to eliminate these courses from all high schools?  Including, say, Groton, Exeter, and the Bronx High School of Science? Or just most high schools?

My fear here is that there is a lazy, unexamined, nasty assumption that we can pretty much assume that certain neighborhoods, groups, cities, and school systems are unlikely to produce the Nobel winners of the future, and that we might as well cut our losses now. Even if this were palatable from the point of view of social equity, I think that the only way to make this kind of prediction confidently is to make it self-fulfilling.

Mathematical/scientific talent is an odd plant – it can blossom in places that never could have been predicted, but drought can kill it early. Let’s not turn the water off just yet.

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