I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world."
When he said this, he was mainly expressing his relief that his work hadn't been used to find newer, bigger, better ways to separate large numbers of people from their lives. Aside from that, it's a nice 'fuck you' to the people who ask the budding mathemagician 'Oh, you study math? What are you going to do with that?
Then there's this one from Richard Feyman, for the Physicists:
Physics is like sex: sure, it may give some practical results, but that's not why we do it.Most budding mathemagicians (and physicists) eventually find 'real jobs' when the constraints of wanting money for food and such force them to do so. Some do become math professors, sure, in the way that some kids fucking around with a guitar in their parents' basement eventually get recording contracts, and some kids eventually get to spend a couple years playing AA, AAA baseball, maybe even making it to the major leagues.
Still, the need and drive to do entirely useless things is strong with the mathematically afflicted (hence this blog). Among other entirely useless and completely unmarketable skills I also juggle, ride a unicycle, and for a while was obsessed with running. Even in my field, I find myself reading about and learning languages I will never use (Haskell), just because they are more interesting than their more established counterparts (Java - simple, practical, mind-numbingly tedious).
In recent years, I have become results-oriented, and to a large degree it's made me miserable. I tend to find getting results entirely unsatisfying. They're a nice by product of doing interesting things, and that's it.