What a fabulous question.
At first, my answer is what I knew math to be growing up. Which is what I consider a system of rules, equations, formulas, etc. I always loved my math, and my brain loved math (even thought I'm a girl!) I loved math every single day until it was conceptual and applied. This is how we teach math today. When I was growing up it was about "knowing your facts" and memorizing formulas or using a "formula sheet" and just plugging in numbers.
Math is SO. much. MORE! As a classmate described working in math, he says doing math involves wearing a tool belt. If you think about when you're working on a project (or a problem) and you use different tools for different things. The tools are put in place to make the project easier or faster. Sometimes you have to try to different tools if you are inexperienced with the project until you find the right tool that works. Sometimes you have a new project and you have to learn what tools to use to do the project. This is how math works.
Math also explains the things that are going on around us. Like when I go to the grocery store and I need to know how much food I can buy. Well, first I have to know how much money I have. To figure out how much money I have, I have to know how many hours I worked and how much money I made for each hour I worked, or the total amount of money I made. Doesn't make sense? Okay, well I want to play outside with my friends after school. But my mom says I need to do chores for 45 minutes and then I need to do my homework for 20 minutes and I also have to read for 30 minutes. And if I want to play with my friends the whole time then I won't be able to watch my normal 30 minutes of TV, but if I want to do both then I'll have to factor that in too. So how long can I play outside in order to make sure I get all my things done... well that's do some math! Now you're getting it!
Math can be proven... and it has been. That's why when we are working with problems today, we get to utilize our tool belt! Because there is proof in the proofs :)