How common is this purity mindset among mathematicians, anyway, where they hope for their math to have no applications whatsoever? I suppose that it’d depend at least somewhat on how one defines “mathematician”. I know that Gauss and Hardy both had that belief; who else, and who didn’t?
I think it’s fairly common for pure mathematicians not to care whether there will be practical applications of their work—that’s not the point of why they do it. Hoping it won’t probably isn’t nearly as common, though more common in times when science and technology are seen as dangerous (e.g. for their use in developing weapons of mass destruction).
What are you basing that on? Gauss did both pure math and applied math/science.
Euclid might be an example.
I doubt there are many pure mathematicians that care about applications one way or the other. There is an undercurrent of humour about the question, and the stream of jokes on the subject add to this. Most mathematicians in the modern world have a wide range of knowledge, and need it.
Perhaps some like the fact that they work in a tiny community with little prospect that their field will suddenly attract attention. Attention where their little community is shattered by the influx of lots of others wanting to get in on the area. There is a lot to be said for research areas where you have happy little workshops with research peers in secluded retreats with good food and wine. Finding your area now has conferences in bland conference facilities in bland cities with bland food and filled with people you don’t know is a real let down.
I don’t think that Gauss believed there was a difference between “pure” and “applied” mathematics.
That is easy to say, but if one applies for a grant from the DOD or NSA it is impossible to keep on fooling oneself.
I am sure that some do, and others like the fact that they, personally, are first on the list every time the New York Times needs a comment or quote about some sexy mathematical topic du jour.
“Here’s to mathematics, the queen of the sciences, and to number theory, the queen of mathematics. May she never find a use.”
I have heard this in the form “Mathematics is the queen of the sciences—and number theory is the queen of mathematics,” for instance when you type “Number Theory” into Wikipedia it shows up right at the top.
However, if one is to claim Gauss actually wrote or said anything of the sort, a shred of evidence would be nice.
Gauss did write that he happened to discover results re. quadratic residues, found them beautiful, and this directly led to him making a profound effort of research in the field. I have not seen where he wrote something disparaging astronomy, whereas he did write a book on the theory of orbit determination.
All this talk of mathematician and physicist sex, including what Randall put into his xkcd comic has me really wondering what exactly is that diagram on the lady mathematician’s whiteboard in the SMBC comic. 