I didn't know anything about this and found the article hard to understand at first, but thankfully the Wikipedia articles on the subject are pretty okay: https://en.wikipedia.org/wiki/Sonnenschein%E2%80%93Mantel%E2...

The very abbreviated TL;DR of this post is:

1. We are taught that markets look like this: https://upload.wikimedia.org/wikipedia/commons/8/8c/Supply-d...

2. By applying rigorous math ("general equilibrium theory"), it turns out that there is no reason that markets can't look like this instead: https://upload.wikimedia.org/wikipedia/commons/a/ab/SMD_Dema...

3. OP's article summarizes how economists have reacted to this problem.