Did Brahmagupta invent the number zero

Invention of Zero and Brahmagupta

I just found out that Zero was invented very close to my home town...

BrahmaGupta who was a great mathematician from Ujjain, an ancient city (est. 6th Century BC) about 40 miles from my hometown Indore (there was no Indore then). This is circa 600 AD.

Arabic scholars adopted Zero and its mathematics from texts written by Brahmagupta (mainly 'Brahma-sphuta-siddhanta' or the 'Corrected Treatise of Brahma'), and was later passed onto Europe through them. The Sanskrit word ‘Shunya’ meaning nothing, empty or void, became ‘Siphar’ (origin of the word Cipher) in Arabic, which became Italian ‘Zephiro’ and hence ‘Zero’ in French and English.

Brahmabupta provided all the rules for adding, subtracting, multiplying and dividing positive and negative numbers. But he made one mistake: he said 0/0=0, which is wrong. As there was no concept of ‘limits’ and differentiation at that time (at least for Brahmagupta), he did not consider that
lim(x->0) x/x = 1. Though even now, mathematicians are unsure about what the value of 0/0 should be. In modern day computer programming languages, it is refered to as NaN or ‘Not A Number’, and dividing by zero is prohibited.

On Astronomy, Brahmagupta argued that the Earth was round and not flat, a point on which he was ridiculed by many Islamic scholars who read his work later.


Aryabhatta

Before Brahmagupta, around 500 AD, another Indian mathematician and astronomer Aryabhatta had said that
"Sthanam sthanam dasa gunam"
or 'place to place in ten times in value'. This might actually be the origin of our modern decimal-based place value notation!

Aryabhatta also influenced the birth of Trigonometry, and he was the first to describe sine's and cosine's, and prepared tables for them.

As with 'zero', the words 'sine' and 'cosine' are derived from what Aryabhatta called them: 'jiya' and 'kojiya'. Arabic scholars called it 'jiba' and 'kojiba'. They were then misinterpreted by Gerard of Cremona while translating an Arabic geometry text to Latin; he took 'jiba' to be the Arabic word 'jaib', which means "fold in a garment", and translated it into L. sinus.

Following Aryabhatta, another mathematician from Ujjain, Varahamira worked on Trigonometry in-depth. He is attributed with first developing basic rules like:
  • sin(x) = cos(/2 - x)
  • sin2(x) + cos2(x) = 1

But, even though Mathematics and Science were quite advanced in India at the time, this progress suddenly ground to a halt after 10th and 11th Centuries. This may be because India was under constant threat of attack from the North and West from descendants of Mongol warlords, and Islamic invaders. With the exception of Akbar, most Muslim rulers of India, favored Persian and Arabic knowledge and culture over traditional ancient Indian knowledge. Hence, such astronomers and mathematicians lost the patronage they used to get during the Gupta kings in the first millenium.

The Gupta period (between 300AD and 600AD) is considered as the 'Golden Age' for Indian science and mathematics. Kings like the legendary Chandragupta Vikramaditya were great patrons of science and art.

Research has always been heavily dependent on state support. Even now, the universities that get most government research grants are also the best in the world. See the earlier post on how Stanford University and the Silicon Valley prospered because of the funding they got for defense projects.

The Wikipedia entry on the history of zero is a good read.

BBC Radio 4 also covered the history of Zero here.