October 31, 2010

How Much Math Do We Really Need?

G.V. Ramanathan, professor emeritus of mathematics, statistics and computer science at the University of Illinois at Chicago, tries to answer this question in the Washington Post. And according to him, you don’t need very much.

Unlike literature, history, politics and music, math has little relevance to everyday life. That courses such as "Quantitative Reasoning" improve critical thinking is an unsubstantiated myth. All the mathematics one needs in real life can be learned in early years without much fuss. Most adults have no contact with math at work, nor do they curl up with an algebra book for relaxation.

First, I commend Ramanathan for highlighting the importance of literature, history, politics and music in everyday life. Such expressions about pursuits generally associated with the humanities are actually not all that uncommon among scientists and mathematicians. However, the favor is too seldom reciprocated by humanists. Second, I think Ramanathan is correct that the current motivations for the study of mathematics are misguided. That said, I disagree with his conclusions. My problem is with the reasons for studying mathematics and not with the conclusion that they need be studied in some depth.

At least two of Ramanathan’s relevant subjects, history and politics, and arguably all four, are pursuits that require math if they are to have positive “relevance in everyday life.”

Let me use politics as an example. Virtually every meaningful political decision from tax policy to reasonable responses to global climate change to war and peace depends in large measure on statistical and probabilistic analyses. And the last time I checked statistics and probability were mathematical disciplines and rather advanced mathematical disciplines at that. I’m not claiming that one needs to do the math to make informed political decisions. I am claiming that one needs to be able to evaluate critically the statistical and probabilistic claims of others. And since as a species, we have really poor and shockingly biased intuitions concerning statistics and probability, we need enough formal training - for most of us that is quite a bit - to recognize those poor intuitions in others and as importantly in ourselves. So what does this mean in terms of a mathematics curriculum? Well, it means a lot more than basic arithmetic. It means considerable algebra, followed by statistics and probability for everyone and not just potential mathematicians. And it may mean more math than that.

I can tell a similar story about history and without too much of a stretch about literature and music also. But I’ll let those go by simply noting that my own appreciation of music is enhanced by my minimal understanding of things like the mathematics of Fourier series and that requires trigonometry as a prerequisite.

I worry that Ramanathan’s piece reflects another example of too narrow a focus on the relevance of an education to individuals and not enough on its relevance to society as a whole. I see education as having a much larger and more important role than any individual may require for their job or in their personal life. The main role of education in a democracy, even a representative democracy, is to make good citizens. It has a political role. And in my mind that requires a lot of math even if few of us will ever use it at work or “curl up with an algebra book for relaxation.”

By the way, I don’t really think anyone can call themselves educated without a basic understanding of Calculus, the Calculus for the purists. The thought process underlying Calculus is so amazing and powerful that it shouldn’t be relegated to mathematicians alone. But then, perhaps not everyone needs to be educated. In a democracy, everyone does need the basic tools to understand the issues and certain aspects of more advanced mathematics are important parts of that tool kit.

Via Slashdot

Posted by Duane Smith at October 31, 2010 2:20 PM | Read more on Current Events |

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Comments

I agree. I am shocked at how little mathematics biblical scholars know. We frequently find commentators claiming that a name was rare in the ancient world, and others claiming that the exact same name was common. None actually give the statistics! This kind of innumeracy would not be tolerated in other disciplines.

It is odd that no-one boast of being ignorant of literature but many seem to make a virtue of their ignorance of simple mathematics.

Posted by: Richard Fellows at October 31, 2010 8:20 PM

More fundamental than mathematics is Logic. In Computer Science, it's vital to understand its principles. In most other fields, it seems, not so much.

So I similarly lament how linguists aren't forced to take intensive courses in logic before obtaining their Bachelor's let alone PhD. In my perfect world, a failure in logic denies *any* chance of passing high school let alone of obtaining a university degree.

Posted by: Glen Gordon at November 3, 2010 4:53 PM

Richard,

Yeah, I agree. One sees some truly awful stuff from Biblical scholars but they are far from alone. The boast of ignorance really drives me nuts and it’s shocking how often one hears it.

Glen,

I tend to agree with your first paragraph but, I do have some concerns about your second one. Formal deductive logic is an interesting exercise and metalogic is really interesting. The problem is that deductive logic depends on initial premises that are derived abductively and/or inductively.

I’ve been in an occasional debate with my daughter, a philosopher by trade and teacher of logic from “critical thinking” to introduction to formal logic to graduate level metalogic, about the language of abduction. I say that the formal language of abduction is modeling but when she tries to pin me down as to what I mean by modeling I begin to stammer. We both agree that the formal language of induction is mathematical probability supported by statistics. I think everyone agrees that the formal language of deductive logic is the predicate calculus plus the various modal calculi (if that’s the correct plural). One thing that I think she, my other philosopher offspring, this one a philosopher of science, and I agree on is that a good math and science sequence does more to help develop logical thinking than all the logic classes ever taught.

Posted by: Duane at November 3, 2010 8:26 PM

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