3 ms·

Nice introduction to group theory. I wish my math profs had used some of this material.

perfect_wave 8y ago
My group theory textbook mentioned the cube briefly, but no mention ever from the professor on it. It really would have helped me in the class because I had a hard time seeing how groups actually apply and why they're so useful. I've gained a lot more appreciation for group theory from exploring math of the Rubik's cube.
tzs 8y ago
I was a second year undergraduate math major at Caltech when the Rubik's Cube came out in the United States, and they quickly seemed to be all over campus. Second year was when we took the intro to abstract algebra course. One of the requirements my professor had was that we each had to do a term project involving material from the class. I couldn't think if anything interesting, so went to to see the professor to see if he had any suggestions for interesting project areas. He simply said "The answer is in your hands". I looked at my hands, and realized I had been carrying my cube with me. Oops. I hadn't even figured out how to solve the stupid thing yet, let alone understand anything mathematical about it, and now my grade would depend on understanding it? DoH! One of the first people at Caltech to figure out how to solve it was Peter Shor. Until there were a fair number of other people who had figured it out, Peter was nice enough to make a nightly circuit of the student houses solving people's cubes for them. I remember one strange night when Peter came around right as several of us where wondering if some particular thing was reasonably do-able. The group wondering this also happened to be high on LSD at the time. (To be clear, Peter was not tripping. He just encountered the tripping group on his nightly cube solving circuit). Both Peter and one of the tripping people started working on the problem. The strange thing was that the tripping person was not a theory guy. He was a strictly experimental cubist. But for some reason he was just staring at his cube thinking about the problem. And Peter, who would usually figure out these things with theory instead was just furiously trying things. Peter and the tripping guy both solved it at the same time, while the rest of us wondered if we had entered the Twilight Zone.

My group theory textbook mentioned the cube briefly, but no mention ever from the professor on it. It really would have helped me in the class because I had a hard time seeing how groups actually apply and why they're so useful. I've gained a lot more appreciation for group theory from exploring math of the Rubik's cube.

tzs 8y ago

I was a second year undergraduate math major at Caltech when the Rubik's Cube came out in the United States, and they quickly seemed to be all over campus. Second year was when we took the intro to abstract algebra course. One of the requirements my professor had was that we each had to do a term project involving material from the class. I couldn't think if anything interesting, so went to to see the professor to see if he had any suggestions for interesting project areas. He simply said "The answer is in your hands". I looked at my hands, and realized I had been carrying my cube with me. Oops. I hadn't even figured out how to solve the stupid thing yet, let alone understand anything mathematical about it, and now my grade would depend on understanding it? DoH! One of the first people at Caltech to figure out how to solve it was Peter Shor. Until there were a fair number of other people who had figured it out, Peter was nice enough to make a nightly circuit of the student houses solving people's cubes for them. I remember one strange night when Peter came around right as several of us where wondering if some particular thing was reasonably do-able. The group wondering this also happened to be high on LSD at the time. (To be clear, Peter was not tripping. He just encountered the tripping group on his nightly cube solving circuit). Both Peter and one of the tripping people started working on the problem. The strange thing was that the tripping person was not a theory guy. He was a strictly experimental cubist. But for some reason he was just staring at his cube thinking about the problem. And Peter, who would usually figure out these things with theory instead was just furiously trying things. Peter and the tripping guy both solved it at the same time, while the rest of us wondered if we had entered the Twilight Zone.