The World of Numbers
Śhūnya: when nothing became a number
Find out how zero became a number, and the rules for using it.
For a very long time the number line started at 1. If you gave away all five of your apples, there was no number for what you had left.
The Babylonians and the Mayans used placeholders: a mark for an empty column inside a number. But they did not treat 'nothing' as a number you could add, subtract or multiply.
Why India was ready for zero. In the Upanishads and in Buddhist writings, śhūnyatā (emptiness) was a state sought in meditation: a mind emptied of all its restless thoughts (vṛttis). Patanjali's Yoga Sutras describe it too. Because Indian thinkers valued emptiness as an idea, 'nothing' could move into mathematics, through Āryabhaṭa and then Brahmagupta.
The Bakhśhālī manuscript, from the early centuries CE, uses a bold dot, a bindu, for zero. "But a symbol is not yet a number." A number needs rules for how it behaves.
Brahmagupta gave those rules in the Brāhmasphuṭasiddhānta (628 CE). He defined zero as what you get when you take a number from itself:
- a – a = 0
- a + 0 = a
- a – 0 = a
- a × 0 = 0
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