As a complement to yesterday's post, I'll offer up one thing about mathematics that has changed my life. I am never bored anymore. There is always a little puzzle to think about. I do some combinatorial research now (it fits well with questions accessible to undergraduates) and so I'm always working on little projects that are advanced by doodling at meetings. I really enjoy mathematics with a visual representation (think ribbon graphs or Young tableaux.). Somehow that visual representation makes it easier to play with concepts while in a faculty meeting or on the bus.
Is this perhaps one reason mathematicians are seen as weird and introverted? This just occurred to me: if we're secretly trying to work out the logical connections between binary strings, Young diagrams, and fixed points of a particular torus action on the Grassmannian we seem far less interested in the company of others than someone who is actually just bored and looking for distraction. Good or bad? Hm!