> Mathematics is a tool that can be used to describe the real world, And that's what the article says the Greeks believed they could do using whole numbers and

> Mathematics is a tool that can be used to describe the real world, And that's what the article says the Greeks believed they could do using whole numbers and fractions. In the case of a real world square with sides of length 1 it seems that you can get away with describing the length of its diagonal in those terms which made it seem odd that it was what caused them to abandon their belief/aspiration. Maybe the author just described their dilemma poorly/strangely. I'm not at all suggesting that math has to be limited to the real world or that irrational numbers don't have their place. We're certainly better off with them.