/sci/ - Science & Math

Okay, so on an informal level all possible mathematical theorems could be arranged in a directed graph, or they could be given a partial order, which indicates dependence.
If someone wants to research mathematics he has to first start high up in the graph and work himself down to deeper and deeper theorems: You have to start with learning sequences, series and babby analysis before you can do research in PDE for example.
Now with every year this graph grows both deeper and wider. But of the graph gets deeper then for any particularily "deep" strand one has tp study longer before being able to add new theorems.
By this heuristic it seems like the depth of mathematics known by humanity is fundamentally limited: If it takes 30 years of study to understand cutting edge mathematics at some point then progress will stagnate.
If this is accurate then only increasing the breadth is possible (new fields).

Do you think this view is accurate?