Step on a crack, break your mother’s back
Solution 1:
It is from an old children's game: if you trod on the cracks between paving stones you were out.
I seem to recall we used to also have the line "step on a line, break your father's spine" in there.
Solution 2:
The meaning is clear in the very first sentence of the article. MIT researchers have found out why concrete breaks down. So, now, cracks in concrete can be avoided. As a result, the sidewalks - made of concrete - would no longer have cracks. And, thus, this saying would no longer be valid for sidewalks.