Oh yeah, great point. Like plugging numbers into the master theorem, if 5x5 could be done in 25 multiplications, say, it would imply multiplication in O(n^2), a

Oh yeah, great point. Like plugging numbers into the master theorem, if 5x5 could be done in 25 multiplications, say, it would imply multiplication in O(n^2), and even 45 multiplications would give a new asymptotically fast multiplication. I would have to dig out a textbook to figure out what an Omega(n^2 log n) lowerbound would imply for n=5. edit of course wikipedia links to a explicit lowerbound which is kind of useful for small cases. https://www.sciencedirect.com/science/article/pii/S0885064X02000079 https://www.sciencedirect.com/science/article/pii/S0885064X0... has it as 2*n*m+2*n-m-2 which is 53 for m=n=5, which is not super tight, but tight enough to say that no 5x5 formula is ever going to lead to an asymptotically faster MM algorithm.