One reason is that people who like to solve this do it for artistic reasons. They do it because they like to, they do it because the approach can be elegant and beautiful. In rare cases analytic solutions lead to generalizations that turn into theorems. I would say that most of mathematics have been created by people's own self-interest in solving problems that many would find "useless".

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"Democracy has proved only that the best way to gain power
over people is to assure the people that they are ruling
themselves. Once they believe that, they make wonderfully
submissive slaves." - Joseph Sobran

Well, in the real world, productivity is key. Especially in the US. Being elegant and such is something to be done in your spare time. The classroom, however, should focus ALL of it's time and energy developing the next generation of problem solvers that can produce results; that can solve the CONTEMPORARY and RELEVANT problems facing humanity RIGHT NOW. If they can do it in an elegant way, cool, but I highly doubt that it would matter at all whether a mathematical model that depicts the way in which humans could reduce levels of greenhouse gases by one half in ten years was elegant.

I'm not bashing your statement. I love math. In my opinion, math is beauty. But im trying to keep the focus of the post.

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There was a time, not that long ago, when the study of prime numbers was seen as pretty useless from a commercial application and benefit point of view ....

(The British mathematician G. H. Hardy (http://www.robertnowlan.com/pdfs/Har...y%20Harold.pdf) remarked:

"Nothing I have ever done is of the slightest practical use."

"No discovery of mine has made, or is likely to make, for good or ill, the least difference to the amenity of the world."

Of interest: prime numbers | How the Queen of Sciences is put to work )

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There are two things you should never try to prove: the impossible and the obvious.

The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low and achieving our mark. (Michelangelo Buonarroti)

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Way to bring it home there, Mr F!

I say you should have encrypted the whole paragraph and posted just the number but I'm annoying in that kind of way.

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"I am beset by the ironies in my life"

In my opinion, I think it is at least beneficial to try and think of an application of what you are doing. For example, Hardy didn't know that prime numbers would be so useful (now its used in cryptology and by banks). So it's good to think of some practical aspects of pure subjects in combination with beauty. That way it has some influence (however little) on society.