As long as we are talking math, you can take a bunch of books and learn the same without need for university. You can even go to talk to somebody who will tell you what books to take and in what order.

What university does is help you connect with other people who study the same, to observe or work with them when solving problems and to have access to people working the cutting edge of the discipline you are studying who you would not normally have access to.

Also, it gives a little bit pressure which might be important for some or most people.

Oh, and official credentials.