for example, matrix multiplication has all sorts of algorithms with exponent significantly less than 3, but they are nearly all curiosities. In practice, the straightforward N^3 algo is used nearly everywhere
I had a long discussion with Rob Pike once that ended with me saying "you know, I don't think people actually use Strassen on supercomputers" (we were discussing how somebody had managed to show an N*2.37 algorithm or something like that and "it was a new world's record").
