Though humans have always understood the concept of nothing or having nothing, the concept of zero is relatively new — it only fully developed in the fifth century A.D. Before then, mathematicians struggled to perform the simplest arithmetic calculations. Today, zero — both as a symbol (or numeral) and a concept meaning the absence of any quantity — allows us to perform calculus, do complicated equations, and to have invented computers.
Early history: Angled wedges
Zero was invented independently by the Babylonians, Mayans and Indians (although some researchers say the Indian number system was influenced by the Babylonians). The Babylonians got their number system from the Sumerians, the first people in the world to develop a counting system. Developed 4,000 to 5,000 years ago, the Sumerian system was positional — the value of a symbol depended on its position relative to other symbols. Robert Kaplan, author of "The Nothing That Is: A Natural History of Zero," suggests that an ancestor to the placeholder zero may have been a pair of angled wedges used to represent an empty number column. However, Charles Seife, author of "Zero: The Biography of a Dangerous Idea," disagrees that the wedges represented a placeholder.
The Sumerians’ system passed through the Akkadian Empire to the Babylonians around 300 B.C. There, scholars agree, a symbol appeared that was clearly a placeholder — a way to tell 10 from 100 or to signify that in the number 2,025, there is no number in the hundreds column. Initially, the Babylonians left an empty space in their cuneiform number system, but when that became confusing, they added a symbol — double angled wedges — to represent the empty column. However, they never developed the idea of zero as a number.
Zero in the Americas
Six hundred years later and 12,000 miles from Babylon, the Mayans developed zero as a placeholder around A.D. 350 and used it to denote a placeholder in their elaborate calendar systems. Despite being highly skilled mathematicians, the Mayans never used zero in equations, however. Kaplan describes the Mayan invention of zero as the “most striking example of the zero being devised wholly from scratch.”
India: Where zero became a number
Some scholars assert that the Babylonian concept wove its way down to India, but others give the Indians credit for developing zero independently.
The concept of zero first appeared in India around A.D. 458. Mathematical equations were spelled out or spoken in poetry or chants rather than symbols. Different words symbolized zero, or nothing, such as "void," "sky" or "space." In 628, a Hindu astronomer and mathematician named Brahmagupta developed a symbol for zero — a dot underneath numbers. He also developed mathematical operations using zero, wrote rules for reaching zero through addition and subtraction, and the results of using zero in equations. This was the first time in the world that zero was recognized as a number of its own, as both an idea and a symbol.
From the Middle East to Wall Street
Over the next few centuries, the concept of zero caught on in China and the Middle East. According to Nils-Bertil Wallin of YaleGlobal, by A.D. 773, zero reached Baghdad where it became part of the Arabic number system, which is based upon the Indian system.
A Persian mathematician, Mohammed ibn-Musa al-Khowarizmi, suggested that a little circle should be used in calculations if no number appeared in the tens place. The Arabs called this circle "sifr," or "empty." Zero was crucial to al-Khowarizmi, who used it to invent algebra in the ninth century. Al-Khowarizmi also developed quick methods for multiplying and dividing numbers, which are known as algorithms — a corruption of his name.
Zero found its way to Europe through the Moorish conquest of Spain and was further developed by Italian mathematician Fibonacci, who used it to do equations without an abacus, then the most prevalent tool for doing arithmetic. This development was highly popular among merchants, who used Fibonacci’s equations involving zero to balance their books.
Wallin points out that the Italian government was suspicious of Arabic numbers and outlawed the use of zero. Merchants continued to use it illegally and secretively, and the Arabic word for zero, "sifr," brought about the word “cipher,” which not only means a numeric character, but also came to mean "code."
By the 1600s, zero was used fairly widely throughout Europe. It was fundamental in Rene Descartes’ Cartesian coordinate system and in Sir Isaac Newton’s and Gottfried Wilhem Liebniz’s developments of calculus. Calculus paved the way for physics, engineering, computers, and much of financial and economic theory.