They found that any Rubik's cube can be solved in 20 moves or less, which doesn't matter. The interesting thing is that although mathematicians and math were involved, and even helped, ultimately the solution was not a mathematical one in the traditional sense.
They just tried every possibility.
To be clear, this is not mathematics as usual. This is the kind of solution that the slow kid in the back does, just plugging through something again and again because he doesn't see the obvious, simple, quick way to know the solution.
In math, you're not supposed to have to use a brute force attack. Sure, a lot of mathematical software uses numerical methods, but this is a case where they clearly would have liked to have found a proof of some kind, but instead just let the computer chug through it. The answer is definitely right, but there's no proof.
It seems like more and more stuff is going this way. It's as if a limit has been reached for human cleverness. Maybe most or all of the new results will come from techniques like this, relying on massive computer power.
Perhaps this will be the new revolution in physics - relativity and quantum mechanics rely on math that is at the boundary of understanding even for people who specialize in it, as far as I can tell. Maybe new methods of doing physics with computers, in a somehow analogous manner, will lead to more progress, as human-generated theories flounder. There's that software that takes raw data and automatically models it, for instance...
I wonder.
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