I've never understood this in mathematics and why it is so revolutionary. How is it a breakthrough when I had an apple, I ate the apple, and now I have zero apples. I'm not trying to be flippant; I really don't get it.
Roman-based numerals do not have a placeholder for "nothing." There was no way to express 1 (apple) - 1 (apple) = 0 (apples). Without the ability to express zero, higher mathematics is cumbersome to the point of impossibility. Without the zero (an Arabic invention) we really could not have algebra (an Arabic word).