Breadth vs. Depth in Maths

Question

As a Maths student (beginning undergraduate), I'm often unable to decide whether to spend my time going in more depth and attempt harder and harder problems (which I do to an extent) or whether I should go on to learn something new or build upon something I already know.

At what "point" should one move on from solving difficult exercises to learning something new? How would you suggest one divides the time they spend on each?

I understand this is subjective and also that a balance is good, but any tips?

Answer 1

Especially in the early years, you should try to get as much breadth as possible. There are many different areas of Mathematics to sample, and you don't know yet which you will find best suited to your interests and abilities. At the same time, you should get practice in doing hard problems, thereby acquiring skills that can be useful in whatever field you eventually specialize in. Exactly how much effort to put where depends on your individual circumstances, which we can't judge from this distance.