I'm also not saying you shouldn't do it. If you love it go ahead, but I believe a field as old as mathematics has a substantial amount of material that you probably will never get through. If anything, at most, all you will do is get summarizations of different branches. In any case, you're going to find yourself favoring a certain branch of mathematics over others, in the same way you favor mathematics over say... evolutionary biology.
It's like saying, I'm going to read every good piece of literature in the world. You can't. You wouldn't even be able to get through the decent books published in the last 50 years. Or even 10 years.
In the long run, it's always best to opt for specialization instead of generalizing.
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