"Doing the Math" by Paul Krugman at the NY Times

[applegrove]

Doing the Math

by Paul Krugman at the NY Times

http://krugman.blogs.nytimes.com/2013/04/09/doing-the-math/?smid=tw-NytimesKrugman&seid=auto

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Wonkblog links to a lovely piece by E.O. Wilson on how much math you need to do research. Wilson’s answer is, not much; and I agree with a caveat. The caveat is this: at least in the areas I work in, you do need some mathematical intuition, even if you don’t necessarily need to know a lot of formal theorems.

Now, both Wilson’s statements and mine should be taken with a grain of salt. A colleague once explained to me that the optimal amount of math for an economist to know is always, of course, exactly the amount of math you personally happen to know — anyone who knows less just doesn’t have the tools, anyone who knows more is excessively teched up. Hey, I think the kids these days are taught way too much math. Also, they should get off my lawn.

That said, I’ve done pretty well with basic calculus plus intuition, mainly geometrical. My most techy paper (and also one of the most successful), on target zones (pdf and very, very wonkish) began with pictures; I didn’t know any stochastic calculus, and picked up the little I needed after I had already figured out the paper’s main results.

But the intuition is crucial, and not just for writing academic papers. If you’re going to talk about economics at all, you need some sense of how magnitudes play off against each other, which is the only way to have a chance of seeing how the pieces fit together. The vast amount of junk economics out there is dominated by people who don’t think that way, who think in terms of slogans — free markets good! printing money bad! — rather than analysis. Or maybe the thing to say is that higher math isn’t usually essential; arithmetic is.

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[applegrove]

1. I too was good at geometry. But not calculus. Algebra I did fine. My intuition was good also.

[Nye Bevan]

2. I bet your geometry teacher was better than your calculus teacher.

And if it had been the other way around you would have been better at calculus than geometry.

[applegrove]

4. Nope. I got 100% in geometry in grade 11. I could work the proofs backwards in one

go. I was a natural. Don't recall any of the proofs as we talk. Calculus needs a big memory for various functions. I was not good at remembering all those.

[napoleon_in_rags]

3. They need to emphasize intuition more.

The reason people have a hard time with calc is that in the beginning they have taking derivatives by hand, which puts you face to face with the biggest algebra equations you've ever seen in addition to the new material. Yet after that, normal people will compute them using a Mathematica. The key is understanding the intuition of what derivative and integral are.