Read general books and surveys; browse a good encyclopedia of math; get a feel
for how the different topics fit together.
I disagree, but not very strongly.
If you find yourself interested in a topic, focus on that topic. Your interest and motivation is more important than being well-rounded or comprehensive.
Most people who are interested in math for itself already know enough that they aren’t going to be too interested in this sort of post. For the majority who learn math for other ends, engineering, computer science, physics, etc, browsing will help them orient themselves, and to find out what interrelationships there are between different fields and techniques. And what they are missing when they discover they need background that they don’t have for a book they are working through.
I disagree, but not very strongly.
If you find yourself interested in a topic, focus on that topic. Your interest and motivation is more important than being well-rounded or comprehensive.
Most people who are interested in math for itself already know enough that they aren’t going to be too interested in this sort of post. For the majority who learn math for other ends, engineering, computer science, physics, etc, browsing will help them orient themselves, and to find out what interrelationships there are between different fields and techniques. And what they are missing when they discover they need background that they don’t have for a book they are working through.