It's fine and nice and wonderful when a part of learning mathematics is chaotic, ad hoc, spontaneous, social, ...
However it would be perhaps of fundamental value to know a very central point of mathematics to which every student would travel; and those who would succeed in attaining it would have an opportunity to continue from this central point in any mathematical direction (and even in more than one).
Even a partial trip toward the point should greatly benefit the student.
Thus what in your (very subjective of course) opinion is the central point of mathematics? Quotations are most welcome too.
Try to make that central place as narrow as possible, let it be a "point". An answer like "Algebra" or "Geometry" or "Mathematical Analysis" would be weak.
REMARK If you don't believe that there is a central point in the whole mathematics then just relax (no need to start a war)--this kind of meta-opinion would be off topic, counter-productive to this thread, one can always start a thread about no point being central. There is a better alternative for any sceptic: even if you don't believe in any center you may still answer my question conditionally, like this: if I have to choose one it WOULD be ...
Actually, I believe that selecting a central point of mathematics would immensely help mathematical education. One would get sharp focus. (The point may move over the time but not too fast).