The bare truth is this kind of mathematics (and, say, theoretical physics) is "hard" and requires a kit of thinking and thus a lot of time. Breakthroughs are na

The bare truth is this kind of mathematics (and, say, theoretical physics) is "hard" and requires a kit of thinking and thus a lot of time. Breakthroughs are named that for a reason -- they involve a distant, non-local solution. If you're doing your research on a topic you will most likely only focus on local improvements to the problems, simply because they lead to more steady results -- they are both safer and don't require you to pretty much think all the time about the problem at hand -- you can't really expect every mathematician to prefer that kind of work.