> I've always theorized that as time progresses the body of work one must be familiar with in order to make new contributions grows as well.
As I see it, this is not too big a problem. Usually people get on a very narrow path and specialize in a tiny part of a larger discipline. There's a lot of new research being done in algebra, analysis, geometry, statistics, whatever; but as a researcher you are expected to choose a very narrow sub-sub -...-sub-discipline and ignore everything else. That's very much doable. An analyst who can't read number theory papers is not a rarity. Likely a rule.
As I see it, this is not too big a problem. Usually people get on a very narrow path and specialize in a tiny part of a larger discipline. There's a lot of new research being done in algebra, analysis, geometry, statistics, whatever; but as a researcher you are expected to choose a very narrow sub-sub -...-sub-discipline and ignore everything else. That's very much doable. An analyst who can't read number theory papers is not a rarity. Likely a rule.