> First, let’s get the obvious difference out of the way. Mathematics is largely a theoretical field. Sure, we can often apply it to the real world, but where’s the fun in that? The goal is not to produce products for ordinary people, but rather to further mathematics as a subject.

I take serious issue with that statement. Many of the most serious mathematicians refuse to think about problems that don't eventually have an application to the real world. It's just that they do it by mapping the real-world problems onto mathematical abstractions, and then studying the properties of these abstractions. (Example: the three-body problem.)