I stumbled across this article last week. I've always wanted to figure out "for myself" how to solve a Rubik's cube. I've also always wondered what Group Theory was and what practical uses it might have for me - reading basic introductions to Group Theory never helped me much because I was never able to apply it to anything.

This article helped me with both - it taught me something about Group Theory in a 'practical use case'. And it gave me some pointers that helped me figure out how to solve a rubik's cube - several decades after I first picked one up as a kid.

In particular, I learned:

  - that if you repeat any sequence of moves enough times, you will always return to your starting position - with hindsight this now seems obvious, which I guess means that I've internalised some new knowledge.
  - that there are 'macros' - sequences of moves that shift just a few 'cubies' and leave the rest of the cube unchanged (I vaguely knew this already).
  - that there is a logical way to make such macros using 'almost commuting' pairs of sequences.
  - why I could never find a macro that swapped the positions of only 2 cubies (because such a move would be an odd permutation of the cubies, whereas moving a side (the basic move you can make with a cube) is an even permutation).
  - how to physically disassemble a cube, so that I could recover the solved cube - very useful when I was getting started with finding macros.

I didn't use the suggested computer solver/visualisation program, but wrote my own rough version - 'for the fun of it' (and also because it didn't run on linux).

Hopefully some others will find this as interesting as I did. If anyone knows anything similar to this for other 'practical' things besides Rubik's cube, I'd love to know about them.