The Story of Zero: How a Symbol for Nothing Changed Everything
For most of history, counting had no way to write 'none'. The idea that fixed it came from India — and it made modern mathematics possible.
Try writing the number one hundred and five in Roman numerals: CV. Now write one thousand and five: MV. Notice something? There is no symbol holding the empty place. The Roman system did not need one, because the letters themselves carried the value.
That works for writing numbers down. It is miserable for calculating with them. Try multiplying CXLVII by XXIII in your head.
The place-value idea
In the system we use today, where a digit sits decides what it is worth. The 5 in 5,000 is worth a thousand times the 5 in 5. But a system like that immediately needs a way to say 'nothing in this column' — otherwise 105 and 15 look the same.
That is the job zero does. It is a placeholder, and then something more: a number in its own right that you can add, subtract and calculate with.
Brahmagupta writes the rules
In 628 CE the Indian mathematician Brahmagupta wrote down rules for treating zero as a number — what happens when you add it to something, subtract it, or multiply by it. Earlier Indian texts already used a symbol for an empty place; Brahmagupta gave zero arithmetic.
The idea travelled: to the Islamic world, where scholars including al-Khwarizmi worked with it, and from there into Europe, where the digits became known as Hindu-Arabic numerals — the ones on your ruler right now.