A Story of Numbers
The Hindu number system
Learn how the Hindu number system, with its zero, came to be used all over the world.
So where does the Hindu system fit? It's a base-10 place value system with ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Read a numeral like 375 by position: (3) × 10² + (7) × 10 + (5) × 1 = 375. Nothing in the symbols says which power is meant; the position does all the work.
And it has had a symbol for 0 since at least 200 BCE. Because 0 is a digit like any other, and exactly one digit sits in each position, no numeral can be misread: 375, 305, 350 and 35 can never be confused. That's the difference from the Mesopotamian system, where a blank could be any size and the placeholder wasn't used at the end.
But the deeper step was to treat 0 not just as a placeholder but as a number, on a par with the rest. That's what Indian mathematics did.
Aryabhata, in the Āryabhaṭīya of 499 CE, used the arithmetic of 0 openly (0 plus any number is that number; 0 times any number is 0) in big scientific calculations.
Brahmagupta, in the Brāhmasphuṭasiddhānta of 628 CE, set out 0 as a number you can add, subtract and multiply with like any other.
By bringing in 0 together with the negative numbers, Brahmagupta created what we now call a ring: a set of numbers closed under addition, subtraction and multiplication (any two of them combine to give another member of the set). Those ideas are the foundation of modern algebra and analysis.
The book sums up the whole journey in five steps:
| Step | Idea | Example |
|---|---|---|
| 1 | count in groups of one size | ukasar-ukasar-urapon |
| 2 | group using landmark numbers | I V X L C M |
| 3 | choose powers of one number as landmarks: a base | 1, 10¹, 10², 10³, … |
| 4 | use position to show which landmark is meant: place value | 1 7 2 9 |
| 5 | 0, as a positional digit and as a number |
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