Yes, we share some parent way up the tree, but we can't go all the way back to that as a starting point because it'd simply take too long to progress from there back down to the interesting leaf node.
This vision makes me wonder when mathematics will reach a point where mastering the material required to understand a leaf node will take greater than the average life span.
I disagree. I observed that, until up to graduation, the situation is like a search graph. When I studied, I noticed many interdisciplinary connections. Fields like mechanic, electronic, logic, automatic, programming, often look like two sides of the same coin.
However I also noticed an inability from others to see the damn connections. If you present the same thing from another angle, they often fail to see it as the same thing, while I factor the obvious pattern like you would code (I've seen it in the case of 3D vision).
The consequences are quite catastrophic: the languages (jargon) used to describe each discipline diverge, making it even more difficult to notice the similarities. This convince even more people that there isn't any connection. That the situation is like a tree. At this point, they don't even bother to seek the connections, and we end up with a disconnected mess.
> This vision makes me wonder when mathematics will reach a point where mastering the material required to understand a leaf node will take greater than the average life span.
That can't happen: more time to study relevant material means less time to push further. It will take many geniuses to be able to learn and push fast enough. But this is pointless. If it takes you a lifetime to learn a particular field, that field will simply fall into oblivion. So, the geniuses (at least the one worth mentioning) won't push further. They will simplify their field, reducing the time required to learn it.