I feel like this is why undergraduate research is absolutely key.
I had the opportunity to work in a lab while an undergrad and to do a couple industry research internships, and it set my expectations on what the Ph.D really is (and why I didn't go for it).
The problem is that many do not know what to expect or have expectations that differ from the reality.
In Math, it's almost impossible to do serious undergraduate-level research. It takes about 2-3 years of graduate level study in a specialty to get to the point where you are at new territory. Almost all the easy theorems have been proven already.
Also, it wasn't until I was in graduate school that I realized people that were comparable/smarter than me were struggling with mediocre jobs or not finding any permanent job at all. I also saw people who were really weak but picked a hot specialty doing rather well.
Also, everything is so specialized in Math that nobody really understand anyone else's work. If everything is so specialized, then how can anyone decide whose work is good and whose work is junk? If objectivity is completely out the window in Math, what hope is there in other areas of science?
So it's essentially the same as being a programmer, where the skill of promoting yourself is more valuable than the skill of doing good work. At least I get paid more, and still have spare time to read about things that interest me.
I had the opportunity to work in a lab while an undergrad and to do a couple industry research internships, and it set my expectations on what the Ph.D really is (and why I didn't go for it).
The problem is that many do not know what to expect or have expectations that differ from the reality.