Nobody needs a number for nothing when they are counting sheep. You have three, or you have none, and none is not a count. That is why the idea of zero came so late, long after people could count into the thousands.
The first use was as a placeholder. Babylonian scribes left a gap, and later a mark, to show an empty column, so that 205 could be told from 25. That is zero doing a job inside a number, not standing as a number itself.
Indian mathematicians, by the seventh century, treated zero as a number you could calculate with. Brahmagupta wrote down rules for adding and subtracting it. From there it travelled through the Arabic world into Europe, where it arrived with the numerals we still use.
1. What Zero Makes Possible
Place value depends on it. Without a symbol for an empty column, 40 and 4 look the same, and column arithmetic falls apart. With it, ten digits can write any whole number, and the same method of adding works whatever the size.
Zero also gave negative numbers somewhere to live. Once nothing is a number, less than nothing can be one too, and the number line runs both ways.
2. Try It
Write 3,050 in Roman numerals, which have no zero, and then write 3,500. Notice how the system copes: it does not use position at all, so it never needs a placeholder, and it never gets to have one.



