Numbers and algebra
AD 628
Zero becomes a number
Brahmagupta
What is nothing take away something?
In India, Brahmagupta wrote rules for calculating with zero and with negative numbers, treating them as numbers in their own right. Together with Indian place-value digits, this is the system the whole world now counts with.
How they figured it out
In 628, in Bhinmal in what is now Rajasthan, Brahmagupta, about thirty years old, wrote a book of astronomy in verse. In it he treated zero, śūnya, as a number with its own rules, and talked about positive and negative numbers as “fortunes” and “debts”.
A debt minus zero is a debt. Zero minus a debt is a fortune. A debt times a debt is a fortune. He even tried to say what zero divided by zero is, and got it wrong (he said zero). Computers today still refuse to answer: they reply “NaN”, not a number. He was asking a genuinely hard question thirteen centuries early.
The equation
Nothing is a number too, with its own rules.
See it in real life
Your bank balance
An account at −₹500 plus a deposit of ₹500 lands on exactly zero. A thermometer at −5 °C that warms by 5 degrees reads 0. Every negative balance, below-freezing temperature and current flowing backwards follows Brahmagupta’s rules.
Where engineers use it
Place value
Every number a computer stores, in binary or decimal, depends on zero holding a place.
Negative numbers
Debts, temperatures below freezing and currents flowing backwards all use Brahmagupta’s rules.
What it led to
- Algebra gets its name c. AD 820
Built on
Al-Khwarizmi’s arithmetic book carried Indian numerals, zero included, to the Islamic world and later to Europe.