The first thing to say about zero is that there are two uses of zero which are both extremely important but are somewhat different. One use is as an empty place indicator in our place-value number system. Hence in a number like 2106 the zero is used so that the positions of the 2 and 1 are correct. Clearly 216 means something quite different. The second use of zero is as a number itself in the form we use it as 0. There are also different aspects of zero within these two uses, namely the concept, the notation, and the name. (Our name "zero" derives ultimately from the Arabic sifr which also gives us the word "cipher".)
The introduction the decimal system in the 13th century to Europeans was the most significant achievement in the development of a number system, in which calculation with large numbers became feasible. Without the notion of zero, the descriptive and prescriptive modeling processes in commerce, astronomy, physics, chemistry, and industry would have been unthinkable. The lack of such a symbol is one of the serious drawbacks in the Roman numeral system. In addition, the Roman numeral system is difficult to use in any arithmetic operations, such as multiplication. The purpose of this site is to raise students and teachers awareness of issues in working with zero and other numbers. Imprecise mathematical thinking is by no means unknown; however, we need to think more clearly if we are to keep out of confusions.
Here's the classic song My Hero Zero from Schoolhouse Rock.
Melvyn Bragg and guests discuss the history of the number between 1 and -1, which has strange and uniquely beguiling qualities. Shakespeare’s King Lear warned, “Nothing will come of nothing.” The poet and priest John Donne said from the pulpit, “The less anything is, the less we know it: how invisible, unintelligible a thing is nothing,” and the English monk and historian William of Malmesbury called them “dangerous Saracen magic.” They were all talking about zero, the number or symbol that had been part of the mathematics in the East for centuries but was finally taking hold in Europe. What was it about zero that so repulsed their intellects? How was zero invented? And what role does zero play in mathematics today?