I have the same question. I would like a nice little Mathematica icon on the desktop with which to launch the application. The icon should be their little spikey guy:
All I can find is a Wolfram icon (which is just the Mathematica kernel, not the notebook interface) duplicated in Education and in Programming. I can find no clickable Mathematica.
I temporarily solved the problem by launching "mathematica &" from a terminal window (you don't need the "/usr/bin" since that's already in your path), and then saved a Mathematica notebook on the desktop. So I can launch Mathematica by double-clicking the notebook. Of course, then I get that notebook.