What is the value of pure math (besides just being awesome?)

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So, as I have stopped focusing on physics and shifted over to math I've found myself much more motivated, happier, and relaxed. Furthermore, I am much better at it. I have not taken any math classes that have been as difficult as the basic E&M physics classes (for me).

I have made such a dramatic shift that I don't even like applied math that much. A better way to say that, is that I don't like applying math, because I'm sure the math that I do has found applications long ago, I just may not be aware of it. A classmate asked what topology could be applied for and I pretty much ignored the professor's response because I don't want to know. It's like knowing that would make the math more "mundane." I just want to play with math things and not give a hoot about the real world. It's all just a game that way.

The reason I have included that tid-bit is because I ask this question not out of a dislike for pure math, but I ask because I genuinely want to know what the value of pure math is to the world, where everything is about dollar signs. Since I completely agree with the idea that math is worth doing for its own sake, I'm not looking for those types of answers. I want to know, in the real world, what kind of value is placed on the math that isn't applied. I want to know where a pure mathematician's paycheck comes from, and why he would be paid. There must be some motivation to pay him, but what is it, if his work is not applied in some real world scenario where a profit can be gained? Or is my view too cynical?

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isn't all sciences derivatives of maths. didnt it all start with maths?
 
  • #3
D H
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Here are two opposing views, both by mathematicians.

I'll start with V.I. Arnold:
Mathematics is part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.
V.I. Arnold solved Hilbert's 13th problem at the age of nineteen. He was a member of that amazingly brilliant set of Russian mathematicians led by Andrey Kolmogorov. This group held that "real" mathematicians had to be adept at everything mathematical, from number theory and topology to turbulence and ballistics.


Next I'll turn to G.H.Hardy, one of the preeminent pure mathematicians of the early 20th century.
If useful knowledge is, as we agreed provisionally to say, knowledge which is likely, now or in the comparatively near future, to contribute to the material comfort of mankind, so that mere intellectual satisfaction is irrelevant, then the great bulk of higher mathematics is useless.
This is Hardy writing in his A Mathematician's Apology. Note well: In this context, apology doesn't mean "I'm sorry". Much closer is the British phrase "bugger off." ("This is what I do. If you don't like it, [strike]I'm sorry[/strike] bugger off.")

Continuing with Hardy's apology,

We have still one more question to consider. We have concluded that the trivial mathematics is, on the whole, useful, and that the real mathematics, on the whole, is not; that the trivial mathematics does, and the real mathematics does not, ‘do good’ in a certain sense; but we have still to ask whether either sort of mathematics does harm. ... There is one comforting conclusions which is easy for a real mathematician. Real mathematics has no effects on war. ... So a real mathematician has his conscience clear; there is nothing to be set against any value his work may have; mathematics is, as I said at Oxford, a ‘harmless and innocent’ occupation.
I can only wonder what Hardy would think were he alive today. The NSA gobbles up pure mathematicians by the lot. Hardy's harmless and innocent pure mathematics in fact turns out to be quite useful in modern warfare.
 
  • #4
SteamKing
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IDK about Hardy, but the NSA would have built Ramanujan his own castle.
 
  • #5
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A pure mathematician is like a poet

An applied mathematician is like a novelist

There is room for both on this earth
 
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  • #6
Demystifier
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Even the MasterCard advertisers understand that money is not the only value:
http://en.wikipedia.org/wiki/MasterCard#Advertising

In fact, money by itself is not a value at all. It is only a tool to buy a true value. Examples are buying food, buying fun, buying poetry, or buying a pure-math book, depending on one's taste.

So the question is not whether pure math has a value (of course it has), but for WHOM it has a value. The answer is that certainly has a value for mathematicians, but in addition there are good chances that a part of it will have a value for others as well.

Take, for example, the Godel theorems. As such, they are pure math without any application. But the work of Godel inspired the work of Turing, which inspired the work of von Neumann, which eventually inspired the construction of real computers.
 
  • #7
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A pure mathematician is like a poet

An applied mathematician is like a novelist

There is room for both on this earth
Okay, I only started college and I am self-studying calculus out of a for dummies book, so I do not know much about pure mathematics; however, there is no way pure mathematics can be as bad as poetry!
 
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Okay, I only started college and I am self-studying calculus out of a for dummies book, so I do not know much about pure mathematics; however, there is no way pure mathematics can be as bad as poetry!
:eek:
You don't seem to know much about poetry either.
(:devil:)
 
  • #9
Demystifier
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"In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite."
Paul Dirac

I guess pure math is somewhere in between. :D
 

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