What's so great about math?

Analysis kind of stuff and rings and fields. How completely useless.

What mathematicians do today will probably come in handy in the future.  Medieval farmers probably would have thought that calculus was retarded and pointless, but it's pretty useful now, and it would have been back then had they used the appropriate technology.  Moreover, it would have aided them in developing that technology, so a good mathematician in the 800s could have done some amazing stuff.

There are many modern applications of algebra (e.g., cryptography, computer science, physics) and analysis (e.g., PDEs with applications in mechanical, chemical, and electrical engineering as well as in chemistry, biology, sociology, and physics, functional analysis with applications in computer science, physics, etc.), but the coolest applications are usually what comes after several generations-worth of seemingly unappliable mathematics.