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Alexandre Borovik wrote a really wonderful http://www.maths.manchester.ac.uk/~avb/pdf/WhatIsIt.pdf" [Broken] on this topic, as a comment and aid in the problem of developing the next generation of creative mathematicians in the UK, his adopted country. He takes a hard cold look at the realities, as indicated by this passage:

If you lke his style, you can read Alexandre Borovik's blog at http://www.maths.manchester.ac.uk/~avb/micromathematics/ [Broken].

This sure resonates with me; in the course of writing my abortive Ph D thesis I generated and proved several good theorems, and oh! it was hard! Not just difficult, but wracking. As the man says, junkies.Mathematicians are sometimes described as living in an ideal world of beauty and harmony. Instead, our world is torn apart by inconsistencies,

plagued by non sequitur, and worst of all, made desolate and empty by missing links between words, and between symbols and their referents; we spend our lives patching and repairing it. Only when the last crack disappears, are we rewarded by brief moments of harmony and joy.

And what do we do then? We start to work on a new problem, descending again into chaos and mental pain. We do that to earn the next fix of elation. Maybe this truth is not for public consumption, but many (and some of the brightest) mathematicians are “problem-solving” analogues of gambling addicts and adrenalin junkies.

My best PhD student once complained to me that she was exhausted, because for two weeks, she awoke every morning with a clear realisation that she continued to think about a problem in her sleep. She was a real mathematician. Where can we find more students like her?

If you lke his style, you can read Alexandre Borovik's blog at http://www.maths.manchester.ac.uk/~avb/micromathematics/ [Broken].

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