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Why Take Math?

This letter from a graduate student was innocent:

Dear Dr. Mankiw,
Hi, I am an undergraduate student studying economics in Michigan. I have recently become a big fan of your blog. I found your "Advice for Students" very helpful to professional economist-wannabes like me, and especially, those considering graduate study in economics. Your suggestion on math preparation for undergrads landed me on one simple question: "Do economists really use all that math?...I look forward to your answer. Thank you in advance!

Best Regards, [name withheld]

Now, some context. Greg Mankiw runs a blog that focuses on "Random Observations for Students of Economics." Mankiw's lengthy responses (and the subsequent blog comments) are great...and should be information shared with students in mathematics classrooms. The connection to economics is irrelevant, as most of the suggestions transfer to any discipline that involves mathematics requirements.

Some key passages from the blog discussion:

  • "Why do we academics want students that have taken a lot of math? There are several reasons:
    [1.] Every economist needs to have a solid foundation in the basics of economic theory and econometrics, even if you are not going to be either a theorist or an econometrician. You cannot get this solid foundation without understanding the language of mathematics that these fields use.
    [2.] Occasionally, you will need math in your job. In particular, even as a policy economist, you need to be able to read the academic literature to figure out what research ideas have policy relevance. That literature uses a lot of math, so you will need to be equipped with mathematical tools to read it intelligently.
    [3.] Math is good training for the mind. It makes you a more rigorous thinker.
    [4.] Your math courses are one long IQ test. We use math courses to figure out who is really smart...."
  • "It's not like they're asking you to eat broccoli or watch the ballet. Math is fun and has the added benefit of being good for you. I'll argue that if you don't enjoy math you don't really enjoy economics. Economics without math is just political science. Yuck." [Ryan]
  • "I disagree with Prof. Mankiw's "take math until it hurts." For most of us math will always hurt, so you need to keep taking it until it doesn't hurt." [JTapp]
  • "The most useful feature of mathematics is the precision with which it forces you to draw out inferences from an explicit set of assumptions. Economists who use the precise language of mathematics to write papers will always benefit, because it is easier for others to both theoretically assess and empirically test the validity of their arguments. In fact, this is the distinguishing feature that has made economics so much more useful than the other social sciences." [Anon.]
  • "Math is the fundamental essence behind everything. Any problem can be solved with math, absolutely any." [Darren]
The discussion continues.... Check out Mankiw's blog for the full discussion, which is a great source of information for mathematics teachers who fight the relevancy issue.