To simplify means to eliminate the unnecessary so that the necessary may speak.
Depending on your experience with mathematics, you may find it hard to believe what I'm about to say. When mathematicians learn something new, they often like to express it in the simplest, most elegant way possible. In doing so, they usually get a clearer understanding of what they learnt, and maybe even discover an interesting relationship to another part of mathematics, or figure out a nice way of improving on what they just learnt.
When I read today's saying, I thought it was a brilliant description of simplicity. I still do. I just don't know what else to say. Perhaps I'll give the last word to Albert Einstein (who was a physicist, not a mathematician).
Make everything as simple as possible, but not simpler.
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