How to think like a mathematician

And why I will never be one . . . witness nostalgic memories of the Rubiks Cube:

It took me 3 weeks the first time, about 1 week the second time. I remember setting my alarm to 5am so I could work on the cube for two hours in the morning before going to school. Eventually I got my time down to a little over 2 minutes (which is just about the longest I can concentrate on anything). There were two kinds of cube solvers: those who held the cube in a stationary orientation and spun the edges around, and those who kept turning the cube around in their hands to get just the right orientation for each move. I was of this second type, which I think kept my efficiency down. One of my math professors in college told me that he'd solved the cube in theory--he taught abstract algebra--but had never bothered to do it in practice. This impressed me to no end. A guy down the hall from me had a 4x4x4 cube, which at one point we tried to see if we could solve using only 3x3x3 operators. I don't think we succeeded.

It's been years since I've done the cube. Last time I tried and tried and tried and got stuck. If I ever want to do it again, I think I'll have to figure out some operators again from scratch.

It came out when I was in grammar school. I solved it once, by extremely long trial and error, and had the wisdom to put it down and never tried to repeat the stunt again. An acquaintance took a more direct method, pulling off the plastic pieces and reassembling them in solved formation. But no one I ever met had a Rubiks Cube theory.