The edifice of pure mathematics is vast and the number of people alive who could give a good overview of existing mathematics as a whole is tiny and possibly zero.

The mathematical experience:

In the 3,000 categories of mathematical writing, new mathematics is being created at a constantly increasing rate. The ocean is expanding, both in depth and in breadth.

By multiplying the number of papers per issue and the average number of theorems per paper, their estimate came to nearly two hundred thousand theorems a year. If the number of theorems is larger than one can possibly survey, who can be trusted to judge what is 'important'? One cannot have survival of the fittest if there is no interaction. It is actually impossible to keep abreast of even the more outstanding and exciting results. How can one reconcile this with the view that mathematics will survive as a single science? In mathematics one becomes married to one's own little field. [...] The variety of objects worked on by young scientists is growing exponentially. [...] Only within the narrow perspective of a particular speciality can one see a coherent pattern of development.