Strassen's algorithm for matrix multiplication

Question

Can someone please explain strassen\'s algorithm for matrix multiplication in an intuitive way? I\'ve gone through (well, tried to go through) the explanation in the book an

Answer 1

Took a quick look at the Wikipedia and it appears to me that this algorithm is a slight reduction in the number of multiplications required by rearranging the equations.

Here's an analogy. How many multiplications in x*x + 5*x + 6? Two, right? How many multiplications in (x+2)(x+3)? One, right? But they're the same expression!

Note, I do not expect this to provide a deep understanding of the algorithm, just an intuitive way in which you can understand how the algorithm can possibly lead to an improvement in calculation complexity.