
This is a book of aspirations fulfilled, those of the author and his colleagues. It tells us what it is to be a mathematician and to do mathematics. It will be read with interest and enjoyment by those in mathematics and by those who might want to know what mathematicians and mathematical careers are like. Halmos, mathematician and expositor, has contributed much to ergodic theory, algebraic logic, operator theory, and the mathematical literature in general.
The average Wikipedia contributor (even ignoring the possibility that they might be a robot) is not an exceptionally good writer, because very few people are exceptionally good writers, because that's what "exceptionally" means.
Paul Richard Halmos
Also well worth a look is Serre's "How to write mathematics badly": https://www.youtube.com/watch?v=ECQyFzzBHlo
This was a very influential book for me in just thinking about what it would be like to do math for a career. And I'm not a mathematician, so I think it worked. :-)
* Paul R. Halmos's "I Want to Be a Mathematician... an automathography: http://www.amazon.com/Want-Be-Mathematician-Automathography-...
* Frederick Mosteller's "The Pleasures of Statistics: The Autobiography of Frederick Mosteller": http://www.amazon.com/Pleasures-Statistics-Autobiography-Fre...
Two more must read books: 1. "The Mathematical Experience" by Davis and Hersh (http://en.wikipedia.org/wiki/The_Mathematical_Experience#cit...) 2. "I Want To Be a Mathematician" (http://www.amazon.com/I-Want-Be-Mathematician-Automathograph...).
Probably the key thing for me in helping my math ability was to actively try to prove theorems. Before reading a proof, I always try to solve the theorem myself first. And then after reading the actual proof... try to prove it again. You'll be surprised how many times you can't prove a theorem for which you just read the proof!!!
But this will help you get better at doing proofs, and understanding math. And it will also help you appreciate good proofs, because you would have already tried to solve it. You'll say, "Ahh... I didn't even think to try that, but that was exactly the step I would have needed".
Lastly, as someone else mentioned -- the proofs you read in texts are polished proofs. Often those theorems proved have been attempted by famous mathematicians who failed to prove it in their lifetimes. Take your time, be rigorous, and thoughtful. If you do that, you come out ahead regardless.