I'm not going to gainsay your experience, but it doesn't match mine. Much of what you do in graduate school is to discover where the accessible areas of research are--where do we have a foothold, and are making progress, and what are some achievable results?
There are big and hairy problems that are bad investments for a young mathematician. I would steer students clear of the Collatz conjecture. But once you get up to speed in your research area, you usually find interesting problems thick on the ground.
Tenure-track positions are competitive, but I don't think there are a lack of interesting things to work on.
when I worked on math I found that no matter what problem I was working on, someone had already solved it completely or to high level of abstraction than I had. got discouraging after while.
Comments
I'm not going to gainsay your experience, but it doesn't match mine. Much of what you do in graduate school is to discover where the accessible areas of research are--where do we have a foothold, and are making progress, and what are some achievable results?
There are big and hairy problems that are bad investments for a young mathematician. I would steer students clear of the Collatz conjecture. But once you get up to speed in your research area, you usually find interesting problems thick on the ground.
Tenure-track positions are competitive, but I don't think there are a lack of interesting things to work on.
when I worked on math I found that no matter what problem I was working on, someone had already solved it completely or to high level of abstraction than I had. got discouraging after while.