I just wish people could forget the idea that Math is fun. It is not. This is anecdotal, but I find at least the math I have learned to be fun. I got a BS in

I just wish people could forget the idea that Math is fun. It is not. This is anecdotal, but I find at least the math I have learned to be fun. I got a BS in math and took some masters-level classes because I enjoyed it. I still work through recreational mathematics and play with project Euler and fractals when I have time. You mention higher levels and more abstract forms of math, and I cannot say I would still have found it fun if I pursued a PHD and tried to truly breach new frontiers, but I can say that my professors generally all told me they enjoyed it. They did it because they had fun with it. Different people find different things fun, but I think its safe to say that some people find even advanced mathematics fun.