Mathematics Throughout History

The Creation of Zero and Pi

How did the concept of zero evolve over time?

The concept of zero developed because it was necessary to have a placeholder—or a number that holds a place—to make it easier to designate numbers in the tens, hundreds, thousands, etc. For example, the number 4,000 implies that the three places to the right of the 4 are “empty”—with only the thousandths column containing any value. Because zero technically means nothing, at first few people accepted the concept of “nothing” between numbers. Not that all cultures ignored the possibility of such an idea. For example, Hindu mathematicians, who wrote their math in verse, used words similar to “nothing,” such as sunya (“void”) and akasa (“space”).

It is thought that the Babylonians were the first to use a placeholder in their numbering system as far back as 400 B.C.E. Instead, it appears they used other symbols, such as a double hash-mark (also called two wedges) as a placeholder. And on a clay tablet found at Kish, an ancient Mesopotamian city east of Babylon, three hooks were used as placeholders—and have been dated to around 700 B.C.E.

Archeologists believe an actual symbol for zero probably started in Indochina or India about the 7th century, but the evidence is scarce. Some scientists believe a crude symbol for zero—resembling a shell—may have been developed by the Mayans independently about a hundred years earlier. While the isolated Mayans could not spread the idea of the zero, the Indians seemed to have no problem. Around 650 C.E., zero became a mathematically important number in Indian mathematics—although the symbol was a bit different than today’s zero.

As for the familiar Hindu-Arabic symbol for zero—the open circle—it would take several more centuries to become more readily accepted. For example, by 1200, the Chinese began to use a sign for zero in their mathematical calculations. And by 1202, Liber abaci (Book of the Abacus) by Leonardo of Pisa, also known as Fibonacci (c. 1170-c. 1250) introduced “0” to Europe, in the famous Fibonacci sequence (he was actually using the sequence in a problem about the reproduction of rabbits). (For more about zero and Hindu-Arabic symbols, see “History of Mathematics” and “Math Basics”; for more about the Fibonacci sequence, see “Math Basics.”)


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