>> “Philosophically we didn’t know before if you can go faster than matrix multiplication,” said Vempala. >> Now we do. > This is the part of computer science

>> “Philosophically we didn’t know before if you can go faster than matrix multiplication,” said Vempala. >> Now we do. > This is the part of computer science that I love. It's a branch of philosophy about what is possible with computing machines. Strictly speaking, if w=2 then their bound of n^{(5 w - 4)/(w + 1)} won't be better than n^w. Since we can't rule out w=2 we still don't know for sure that solving sparse systems is strictly easier. However this is a good indication.