[bo1024]

There's a big difference between being one of the only ones in a field because it does not yet exist (i.e. you are founding the field) and because it is exhausted (i.e. all the big results are already proven).

[thaumasiotes]

It is generally not the case in any area of math that "all the big results are already proven".

[bo1024]

True. But, well, for instance, all the finite simple groups are classified.

(Not in the sense of the NSA.)