If you're working in a field of mathematics that is not driven by real world problems (or the abstraction of real world problems), then how do you gauge the value of your work? How do you decide what is important to work on? Is it purely on a whim?
value of work in mathematics
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soft-question
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3As with all things related to "value," it really depends on your values. – 2012-09-27
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2A related question on MathOverflow: http://mathoverflow.net/questions/39828/how-do-you-decide-whether-a-question-in-abstract-algebra-is-worth-studying – 2012-09-27
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1The beginning answers to this can be found in G.H. Hardy's "A Mathematician's Apology." – 2012-09-27
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1I never cared about such judgements; I simply did what interested me. I always felt that my real work was teaching anyway. – 2012-09-27