'Right,' said Colon....'I heard this wizard down the University say that the Klatchians invented nothing. That was their great contribution to maffs, he said. I said, "What?" an' he said, they come up with zero.'
'Dun't sound that clever to me,' said Nobby. 'Anyone could invent nothing. I ain't invented anything.'
-Terry Pratchett JINGO p.29
(via a comment from samart, thanks!!!)
So Brahmagupta has come up with his fascinating theories about zero in India, and various tradespeople and explorers have transported these ideas (along with their spices and so forth) back to Baghdad and the rest of the Middle East.
The most famous of the Muslim mathematicians to use the new zero in his work was Mohammed ibn-Musa al-Khowarizmi (the gentleman on the stamp). He "invented" or at least coined the term for algebra ("al-jabr" means "completion").
In any case, al-Khowarizmi investigated linear and quadratic equations equal to zero. He made enormous strides in demonstrating the great practical use of al-jabr and ultimately of zero, not simply as a placeholder but as an extremely important number in its own right (read more about al-Khwarizmi).
As a brief aside, in algebra one of the most exciting things about zero is its remarkable multiplicative property. Anything multiplied by zero is equal to zero, and (crucially for quadratic equations) if the product of any two numbers is zero then one of them has to be zero.
Interesting though it is, this doesn't get us much further in the story. The next player to enter the scene was a little boy called Leonardo. His father was a customs officer and merchant from Pisa, and young Leonardo would accompany him on his trips in North Africa and the Middle East. Leonardo grew up to write a book called Liber abaci, in which he explains the Hindu/Arabic numerals, including zero. You've probably heard of Leonardo. He's better known as...Fibonacci! (read more about Fibonacci).
Since Fibonacci was Italian, this brought zero firmly into the European sphere of thought. As is usual with revolutionary ideas, the private sector cottoned on to the wonderful properties of zero quickly, while governments and officaldom in general was more suspicious.
However, the work of several influential mathematicians (including Descartes) gradually brought zero into common usage. Eventually Newton and Leibniz were to find it indispensible to the furtherance of calculus...
And now...well, can you imagine maths, or life for that matter without zero?
I certainly can't!
By the way, go here for a wonderful discussion of the history of zero in general...This is where I got a lot of my inspiration for this mini-series.