Comment by pontus

I think the OP was pointing out that the reason Strasssen's algorithm works is that it somehow uncovered a kind of repeated work that's not evident in a simple divide and conquer approach. It's by the clever definition of the various submatrices that this "overlapping" work can be avoided.

In other words, the power of Strasssens algorithm comes from a strategy that's similar to / reminiscent of dynamic programming.