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A mosaic detail on “The Standard of Ur”, c.2600 BC, made in the city where the “positional system” was invented (MICHEL WAL CC BY-SA 3.0)



Who invented zero? Certainly not the Greeks and Romans. When the Romans used a count-down they ended with 1, not 0. For example their calendar counted down to the Ides in the middle of the month, the previous day being “the day before the Ides”, and the day before that being “the third day before the Ides” — rather than the second day before. They had no concept of 0, and the New Testament of the Bible, written in Greek, tells us that after the crucifixion “he rose again on the third day”, meaning two days later. Church scholars had determined that the day of the crucifixion was a Friday, so “the third day” meant Sunday (two days later), hence the Christian choice of Sunday as the holy day, rather than the Jewish Sabbath. In the Classical world counting — up or down — started or ended with 1. There was no zero, and no year zero: 1BC is followed immediately by 1 AD.

European mathematics only adopted the concept of zero in the 13th century after the publication of Liber Abaci (book of computation) by Leonardo of Pisa, aka Fibonacci. He used the Arabic numeral system, learned from North Africa. The shape of the digits was rather different from the customary Western forms, but the point was that the order of the digits in a number determined its value. You did not simply add together the value of digits representing 1 up to 9, 10 up to 90, 100 up to 900, etc, as in the Greek system. For instance, 327 is not the same number as 273. This is the “positional” or “place-value” system, a fantastic advance on the previous methods of writing numbers used in Europe and the Classical world.

Thus in his 1911 book An Introduction to Mathematics the philosopher Alfred North Whitehead applauded our modern notation for numbers:

By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases the mental power of the race. Before the introduction of the Arabic notation, multiplication was difficult, and the division even of integers called into play the highest mathematical faculties.

His term “Arabic notation” refers to the positional system, which the Arabic world acquired from India where it had been in use since the 6th century BC. In modern parlance we talk of Hindu-Arabic or Indo-Arabic numerals, which use just ten digits including zero to represent all counting numbers. A brilliant system, it was later extended to decimal fractions, with a decimal point separating the fractional part of a number from the rest.

This is the accepted narrative, but neither the Arabs nor the Indians invented the positional system with its inevitable use of zero. That honour goes without question to the Sumerians, inhabitants of southern Mesopotamia since before the dawn of history. They invented writing on clay tablets, starting in the late 4th millennium BC in the city of Uruk, home to the legendary Gilgamesh, and origin of the modern name Iraq. In 3000 BC Uruk was the greatest city in the world but during the 21st century BC that role belonged to the city of Ur, where the “positional” system of writing numbers was invented.
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