Brahmagupta: The Mathematician Who
Defined Zero in 628 CE
Before Brahmagupta, zero existed as a placeholder — a symbol to distinguish 10 from 1, 100 from 10. No one had formally defined what zero is as a number, or what happens when you add, subtract, multiply, and divide with it. Brahmagupta did. In Sanskrit. In 628 CE.
His text, the Brahmasphutasiddhānta, contains the first systematic treatment of zero and negative numbers in mathematical history. The rules he wrote are still the rules taught in school today — almost word for word, 1,400 years later.
Brahmagupta's Rules — Written in Sanskrit
शून्यं शून्ययोगे
"Zero added to zero is zero"
The first formal statement in history that zero added to itself yields zero — establishing zero's additive identity property.
धनर्णयोः शून्यम्
"A positive and a negative [of equal magnitude] yield zero"
The first written rule for additive inverses — the foundation of all signed arithmetic.
ऋणं ऋणे धनम्
"Negative multiplied by negative is positive"
Written 1,400 years ago. Still taught in every school on Earth.
शून्यभक्ते शून्यम्
"Zero divided by zero is zero"
Brahmagupta got this wrong — we now say 0/0 is undefined. But the attempt to define division by zero was itself revolutionary.
Brahmagupta's Formula for Cyclic Quadrilaterals
Beyond zero, Brahmagupta derived a formula for the area of a cyclic quadrilateral (a four-sided polygon inscribed in a circle) that generalises Heron's formula. It is still called Brahmagupta's formula in mathematics textbooks worldwide: Area = √((s-a)(s-b)(s-c)(s-d)) where s is the semi-perimeter.
He also described what is now called the Brahmagupta–Fibonacci identity, linking the product of sums of squares — a result independently rediscovered by Fibonacci in 1225 CE, nearly 600 years later.
Source: Kim Plofker, Mathematics in India, Princeton University Press (2009)
"Brahmagupta's work is a landmark in the history of mathematics. His treatment of zero and negative numbers was without precedent in any earlier mathematical tradition."
— George Gheverghese Joseph, The Crest of the Peacock, Princeton University Press (2011)
Sources
- • Brahmasphutasiddhānta (628 CE), Chapter 18 — translated by H.T. Colebrooke (1817)
- • Kim Plofker, Mathematics in India, Princeton University Press (2009)
- • George Gheverghese Joseph, The Crest of the Peacock, Princeton University Press (2011)
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