TITLE: Fast matrix multiplication
QUESTION [36 upvotes]: Suppose we have two $n$ by $n$ matrices over particular ring. We want to multiply them as fast as possible. According to wikipedia there is an algorithm of Coppersmith and Winograd that can do it in $O(n^{2.376})$ time. I have tried to look at the original paper and it scares me. It seems that it is impossible to understand current state of the art.
So, the question is the following. Is there any 'gentle' introduction or survey for beginners in this particular field? I took only introductory course in algebra, so it would be nice to know what parts of algebra do these techniques rely on.

REPLY [3 votes]: A recent article by Kevin Hartnett in Quanta magazine (Matrix Multiplication Inches Closer to Mythic Goal) is targeted at (math-inclined) laypeople and discusses the recent result of Josh Alman and Virginia Vassilevska Williams (A Refined Laser Method and Faster Matrix Multiplication) where they obtain the bound 2.37286.