I was thinking about this today and it seems like a good question. Assuming mathematics will keep on expanding, do you think it will ever become impossible for a beginner to learn all the known material on a subject (such as mechanics), simply because there is so much prerequisite material to learn? Of course, this will have to be in the very far future, because at the moment we can still get talented 15 year olds up to speed due to the compressed material available in textbooks, which contains centuries worth of research in a few hundred pages.
Hope you understood my question, any replies are appreciated.
I think this question is quite analogous to this one:
Will it become impossible to learn music?
One can argue quite convincingly that some branches of music have a deep theory, and to master it (in a certain technical sense) is almost impossible. But the point is: music isn’t about mastering an aspect. It’s really about interconnecting experiences in order to add, increase and even modify the existing “theories”. In mathematics, where the knowledge builds up on itself most explicitly when compared to some other fields, it is common to think that it is a characteristic of mathematics itself: the neverending things to learn about something; there is always something more about the subject. But this isn’t exclusive to mathematics at all. Everything always has something else. So, in some sense, the answer to your question is yes.
… But humanity always finds something new. New concepts, new ideas, new ways to think about something. This is where the analogy to music kicks in: some people, for example, may have thought that classical music closed it: we have all we need. Then came jazz. Some professors may have thought that physics was closed: we have all we need…
“in this field, almost everything is already discovered, and all that
remains is to fill a few holes.” – Quote from a professor to Max Planck, advising him not to study physics. Planck was one of the prominent names of quantum physics.
We are humans. We will always come up with some new crazy stuff. This answer your question as a no: because we will always create new things to learn.