Comment by zem

to get some intuition about why this is such a big deal, look up the history of strassen's algorithm, which solved matrix multiplication in less than O(n^3). this was a truly stunning result because it seemed intuitively obvious that the output matrix had n^2 cells each of which was calculated via an independent O(n) loop over a row/column of the input matrices, so how could you do better than n^3. but once strassen proved that you could do some clever tricks and reduce the overall time to something less than O(n^3) it started an entire cottage industry of people getting better and better algorithmic bounds. the initial breakthrough was a qualitative one, independent of how much it improved things in numerical terms.

https://hideoushumpbackfreak.com/algorithms/algorithms-stras...