Zero

Judging by the bookshelves at my neighbourhood bookstore, the concept of zero seems to be one of the more popular concepts in popular recreational mathematics nowadays. (see this article from the American Mathematical Society's Math Digest for a bit more info). Perhaps the reason for this is that of historical interest, as the exact origins of the concept are foggy, and that zero was not accepted in many mathematical circles until rather recently.

One important thing to notice about zero is that there are two uses of zero that are both important (although important for different reasons) but are different. The first use of zero is as a placeholder in a positional numeral system. For example, 381 is a completely different number from 30810. The second use of the number zero is as a number, in the form "0". It is unclear exactly when zero was first used in either of these two roles.

The use of zero as a placeholder probably first occured in ancient Babylon. Surprisingly, even though the ancient Babylonians used a positional number system, they did not use zero as a placeholder until relatively late in their history.

The use of zero as an actual number probably originated in India. In the 7^th century A.D., the mathematician Brahmagupta considered zero a number in his works and even gave rules for handling it in calculations.

In Europe, it was not until the 1600's when zero finally started to become accepted as a number.