Both are equally important and equally beautiful as they both are mathematical structures. Intrinsically mathematics is  not only useful but beautiful as it is a study of patterns, axiomatic and logical structures enshrined with elegant proofs of rigor. Who thought the imaginary numbers have physical application when they were introduced ? The very reason they were called imaginary was because it was believed they are just figments of our creations which have no real meanings at all. The same thing with the Dirac operator wich by many  now is treated as the actual operator in the language of nature. 

 Lovachevsky summed it by saying " no part of mathematics however abstract it may be that will not be put to the service of science and mankind  in near or distant future " The mathematical facades and structures that are built theoretically and strengthened by passionate mathematicians will some day find a perfect and indispensable demand and applications in sciences. It is therefore equally imperative to work and augment the galaxy of mathematics.

Despite the beauty of mathematical solutions must ultimately a benefit coming out, whether sooner or later does not matter. In our present society the art of mathematics will be a nice adjunct to the technical / economic solution pathway. Unlike many other arts, the beauty of mathematics will also be recognized only by the sovereigns of this science.

Dear Dejenie A. Lakew,

I enjoyed your answer. Of course, I have already known about the history of complex and "imaginary" numbers. Beautiful idea about the structures built by passionate mathematicians.

Best regards,

Sandor

Dear H.-P. Schulze,

Following the comments of Dejenie A. Lakew and Lobachevsky of course, I strongly believe that elegant results will be used sometimes for something. Maybe a few decades, few centuries, or few milleniums later... Who knows? From this point of view, it is just a matter of perspective whether to insist on the benefit or not. I would not like a world where everybody writes mathematics with a benefit only in mind. Ultimately, this would be harmful for the "benefit" itself. I like to think about mathematical results as a library of knowledge which will be used or not, but at least we have a variety of things to choose from. I have several books in my library which I have never opened, but it "calms my soul" knowing that I could open them sometimes, but I am not forced to do so. If we restrict ourselves like businessmen for the impact only in mind (as George Stoica said above) then mathematics would become much poorer and that would not benefit anybody, strangely not even the people who care only about immediate impact.

Best regards,

Sandor