There is also no Nobel Prize offered for Newspapers. So? Your standpoint was that mathematics without use is not published, and your justification for this is there is no Nobel Prize for Mathematics? Bizarre. Or do you mean that mathematics is not justified without application, and the reason for this is that there is no Nobel Prize? Only things worthy of winning the Nobel Prize are publishable/worthwhile?
There are many speculations as to why there is no Nobel Prize for mathematics, ranging from the stupid (Nobel's wife had an affair with a Mittag-Leffler and he never forgave the subject. Nobel wasn't married), to the vaguely plausible (he just forgot) to the not unreasonable (he viewed mathematics as a tool of the other sciences, in analogy there is a literary prize, but no prize for the philologists). Given the period when Nobel founded the prize, it is the last of the 3 that is preferred by me, at least.
Mathematicians' research then was primarily motivated by the applied sciences. Even something as obtuse as homological algebra has its origins in the study of planetary motion. The divergence from this to purely abstract topics started rigorously around the 20's when people had digested the implications of Cantor and Goedel. Please, do not think this is authoritative, merely illustrative. The study of abstract mathematics leads to some amazing results, that only now the physicists are getting interested in again. Things we did without the need for real life motivation. It is perfectly acceptable to have this parallel development of ideas. Indeed, I am continually surprised by the sheer distaste shown by people who like to think themselves educated in the physical sciences towards pure mathematics.
If you don't think it can be useful, I suggest you read about the current interests in theoretical physics a la Witten for triangulated categories. Things we in our little world of pure maths have been studying for decades. And don't forget that Galois invented Groups in order to examine the roots of polynomials, and now we find them describing elementary particles, gauge theories, symmetries, spectral theory of chemicals, crystallography, cryptography, coding, random walks...
Oh, and there are at least 30 published papers on my desk that weren't written with the slightest interest in applying the results to anything in the real world. I can walk down to one of the Libraries here and find shelf after shelf of journal publications all written without application to the real world. I can think of a section where there must be 50,000 pages of abstract logic publications. Who'd've thought that the philosophical musings of, say Russell (Nobel Prize winner, Literature 1950), would be the basis of one of the most important aspects of our modern world - all computing is essentially predicate logic.
By all means carry on thinking that you're opinions about modern mathematics are correct because you can back it up with those of someone who was born in 1833. (As someone else may have pointed out in the many articles about this, Nobel didn't offer a prize for genetics, did he?)
We now also have the Abel Prize for Mathematics. The first was won by J.P. Serre, in 2001, the second by Atiyah and Singer for their Index Theorem, which showed how to use the machinery of abstract pure mathematics in physics. Both men trained as pure mathematicians, though increasingly many of us find such disttinctions unhelpful and prejudicial. I can't think why.
