March 28th, 2014, 04:04 PM  #1 
Newbie Joined: Mar 2014 Posts: 13 Thanks: 6  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? 
March 29th, 2014, 04:29 AM  #2 
Senior Member Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108  
March 29th, 2014, 07:05 AM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
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.) pushups are useful, because they understand that people doing that exercise aren't interested in being better at pushups 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. Last edited by CRGreathouse; March 29th, 2014 at 07:09 AM. 
April 3rd, 2014, 05:15 AM  #4 
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22 
Well, one thing I am fond of saying: If you want to commune with the infinite and eternal, open a math book.

April 3rd, 2014, 07:31 AM  #5 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  
April 3rd, 2014, 09:08 AM  #6 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory 
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. 
April 3rd, 2014, 09:55 AM  #7 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  
April 3rd, 2014, 10:23 AM  #8  
Senior Member Joined: Dec 2013 From: Russia Posts: 327 Thanks: 108  Quote:
On the other hand, I've just looked at the article describing the persective of hightech 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 highschool mathematics in their profession is pretty low. 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.  
April 3rd, 2014, 12:00 PM  #9  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Quote:
I'll leave this here just in case: CompCert  Main page  
April 3rd, 2014, 05:29 PM  #10 
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  

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