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March 28th, 2014, 04:04 PM   #1
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The Misconception About the Need for Learning Mathematics

So, here's a discussion topic I could put in here. All the time throughout middle and high school, whenever I would be in a math class, I would keep hearing some student say "We don't need to learn this" or even go as far as to asking the teacher, "Why do we need to learn this?" I have a perfect answer for this, but I would rather hear it from you guys.

How would you respond to such a question as this one?
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March 29th, 2014, 04:29 AM   #2
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"Why do we need to learn this?"
For mind training. I agree that many students don't need the subject matter per se.
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March 29th, 2014, 07:05 AM   #3
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One reason is the 'unreasonable effectiveness of mathematics': you never know when you will need something, even when it seems like it would never come up.

Another reason is to train your brain generally. No one asks why (e.g.) push-ups are useful, because they understand that people doing that exercise aren't interested in being better at push-ups per se but rather at becoming stronger.

As an example of the former, I once coded the Lambert W function for PARI/GP (see my .sig below). I didn't have any purpose for it but to improve that system -- I figured it was a neat special function to add. But when I later wrote a (fairly) efficient implementation of the Bell numbers I found I needed to use the W function, and so it was unintentionally useful to have one laying around.
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April 3rd, 2014, 05:15 AM   #4
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Well, one thing I am fond of saying: If you want to commune with the infinite and eternal, open a math book.
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April 3rd, 2014, 07:31 AM   #5
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Well, one thing I am fond of saying: If you want to commune with the infinite and eternal, open a math book.
If you want to retain faith in humanity, you probably shouldn't discuss the infinite with non-mathematicians.
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April 3rd, 2014, 09:08 AM   #6
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This I encounter very often. My usual answer is "you never know when you need something" and then I bet that they can't tell me a branch such that I can think of no real application.

I win, of course! C'mon, tell me a branch of mathematics -- craziest and the most pure you can think of -- and I will always give you one (or more, mostly) applications in the real world.
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April 3rd, 2014, 09:55 AM   #7
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C'mon, tell me a branch of mathematics -- craziest and the most pure you can think of -- and I will always give you one (or more, mostly) applications in the real world.
MSC 46B08: Ultraproduct techniques in Banach space theory.
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April 3rd, 2014, 10:23 AM   #8
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This I encounter very often. My usual answer is "you never know when you need something" and then I bet that they can't tell me a branch such that I can think of no real application.
The word "you" in "you never know" is plural; more than that, it refers mostly to the society as a whole than to some groups of people. Yes, it is probably reasonable for the US National Science Foundation to support all promising mathematical research, no matter how abstract. As you say, such research often finds unexpected applications, and they are likely to turn out useful in such economy as the US.

On the other hand, I've just looked at the article describing the persective of high-tech business in Russia. The conclusion is that high tech is used in the military, but most of the Russian economy is based on relatively low tech production such as oil industry and construction. I have not researched this issue, but unfortunately it is extremely common for college graduates in Russia to work not according to their major. Many graduates of math departments become at best programmers or work in the financial industry. In these consitions, the probability that any single person will use even high-school mathematics in their profession is pretty low.

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C'mon, tell me a branch of mathematics -- craziest and the most pure you can think of -- and I will always give you one (or more, mostly) applications in the real world.
OK, tell us how the part of set theory that studies sets with cardinality greater than continuum is used in real life. In my opinion, it is at best used indirectly: as a theoretical foundation for other areas of math that have more direct applications. The one exception that I know of is probably developing and justifying methods for verifying computer programs. Even if programs deal with natural numbers only, to handle programs in all generality requires a suprisingly hard and abstract mathematics.
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April 3rd, 2014, 12:00 PM   #9
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The one exception that I know of is probably developing and justifying methods for verifying computer programs.
...but that exception is big enough to drive a truck through it, so you're kinda making his point here.

I'll leave this here just in case:
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April 3rd, 2014, 05:29 PM   #10
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If you want to retain faith in humanity, you probably shouldn't discuss the infinite with non-mathematicians.
Good point!
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