Just to add something to your point: I think that gaining mathematical experience and knowledge or traing or whatever also improves your songwriting skills. By saying this I do not mean that you have to be a fat math nerd to play well guitar, I mean that it widens your borders of perception, you are able to make interconnections between ideas much more easily if you have that thing. Basically I am conviced that people with math type of brains are able tomake more original music than people with music type of brains nowdays. I say this because I think that musical shapes that are appealing to the ear are being used as music has undergone through so many stages and every chord progression seems familiar. In this respect I think that a mathematical kind of person is able in a better way to find his niche(sp?) in todays music. And again, I am not talking about those mathematical guys that are nothing more than that and have no other interests than solving math problems and playing Warcraft and etc.
About books: I think its great to read a lot but I just do not have time for it, since I am working fulltime right now and when I get home I just have energy to grab my guitar for 2 hours or so and throw some stuff on my computer. I feel that there are huge holes in my culture, in terms of knowledge of literature, philosophy, music which I would like to fill up. It appears thought that I'll be going just in the opposite direction since I'll be studying some Engineering in Germany(possibly in Hamburg).
The world is loaded, it's lit to pop, nobody is gonna stop!