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September 18th, 2014, 08:14 AM  #1 
Newbie Joined: May 2014 From: InOnePlaceorOther Posts: 21 Thanks: 1  What good is a (pure) mathematician?
I don't mean this question to offend, but it seems like the right wording to me. I am wondering: if one studies math and becomes a mathematician, and tries to solve the equations unsolved for mankind or tries to develop new systems or new questions, what in truth has he done? I suppose we don't know what we don't know, so one can't calculate the value of an unknown, but what does one expect to find? What has math brought us except ways to better understand physics and engineering? (This is not an attack, I am just saying I don't know. It has never been apparent to me. Thanks for any responses) 
September 18th, 2014, 10:03 AM  #2 
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 
Hardy's Apology is a standard answer here. To butcher his argument (please read the original, you can find it online): math should be appreciated for its beauty and the fact that it *doesn't* lead to people making better and better ways of killing each other (apparently he was pretty affected by WWI). Wigner's "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" is another common view. Again, read the original, but mathematics has led to many important discoveries which were unforeseen at the time. On the particular question of pure vs. applied, I think Hardy's quote is apt: Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics. Last edited by skipjack; October 4th, 2014 at 03:20 AM. 
September 18th, 2014, 05:08 PM  #3  
Senior Member Joined: Aug 2012 Posts: 1,956 Thanks: 547  Quote:
What would he make of the fact that in the past 20 years, number theory has become the basis of computer encryption; and that many of the world's great number theorists work in secret for the NSA, spying on the people of the world?  
September 18th, 2014, 06:16 PM  #4 
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 
Oft asked, rarely answered.

September 19th, 2014, 06:37 AM  #5 
Member Joined: Aug 2014 From: Somewhere between order and chaos Posts: 44 Thanks: 5 Math Focus: Set theory, abstract algebra, analysis, computer science 
Well, pure mathematics has many applications to the technology we use, which greatly improves our quality of life. Aside from its practical applications, the study of mathematics also teaches you to think logically and analytically, which is useful in all areas of life. But on the whole, the "What is it good for?" comment can be applied to just about everything. What is art good for? Do we actually need it? What do we gain from looking at pretty pictures? What do we gain from listening to music, reading literature, etc.? What is science good for? What practical benefit do we gain from knowing that humans evolved from apes, or that atoms are made of protons, neutrons, and electrons? Pretty much every discovery or achievement made by humanity is altogether useless, when you take a purely pragmatic view of it. 
September 19th, 2014, 08:16 AM  #6  
Member Joined: Aug 2014 From: Somewhere between order and chaos Posts: 44 Thanks: 5 Math Focus: Set theory, abstract algebra, analysis, computer science  Quote:
 
October 1st, 2014, 06:39 AM  #7 
Newbie Joined: Mar 2014 From: Manchester, United Kingdom Posts: 11 Thanks: 4 Math Focus: Number Theory 
What good is a pure mathematician? They are excellent lovers. 

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