The History of Zero
By Steven Glicksman and Paul Glicksman
The number zero is not awarded much glamour in daily life. Most people do not appreciate the importance of zero, other than they want lots of them behind other numbers in the calculation of their net worth.
The etymology of the word zero is complex. Zero comes from the French translation of the Italian word “zefiro,” which was coined by Italian mathematician Fibonacci (c.1170-1250). Considering that Fibonacci grew up in Arab North Africa, this is likely the mispronunciation of the Arabic word “safira” meaning empty. Scholars also point to the Sanskrit word “sunya,” meaning void, as another possible origin of zero. The significance of these theories is that zero was not invented independently by multiple civilizations, but was brought to Europe by traveling Arab traders from India, and disseminated around the globe. In actuality, zero is thought to have been developed as early as the 6th century by the Gupta Dynasty in India.
The fact that it took so long for humans to realize that zero was a number is both understandable and astonishing. Zero is not mentioned in the Old Testament. It was not understood as a number by the ancient Egyptians. The Greeks, who pioneered geometry and philosophy, did not have the concept of zero. The Roman Empire’s achievements in architecture and engineering did not include zero.
To a modern observer, the concept of zero is fairly simple and logical. It seems like it would be quite obvious to any caveman that if he had no berries, then he had zero berries. If he had two rocks, but two were taken away, he now had zero rocks. However, for the bulk of human history there was never any distinction made between nothing and zero. In other words, zero was seen as a lack of number rather than a number by its own right.
Think of the subtleties. If you have no losses, then your loss ratio is zero. But what is your loss ratio if you have no losses or premiums?
The origins of zero appear to have derived from the necessity of a numerical placeholder rather than inspired mathematical thought. In the earliest systems of numbers the number zero was not required. These schemes were called “additional” number systems because symbols are added. For instance, in the old Roman numbering system I stood for 1, V for 5, X for 10, etc. The symbols were combined, such as XV being 15. There was no need for a zero because, in the Roman mind, what would be the purpose in adding nothing?
The advent of “positional” number systems changed this thinking. Positional systems work on the modern principle of assessing a number’s value based on the position of the numbers that compose it. In our system, 456 gets its value from 4 hundreds, 5 tens, and 6 ones. The only problem with this order is that, sans zero, the number 202 would be no different than 22. As a result, several place-holding mechanisms were invented. In China, spaces were used to denote position. In Babylon, a separate symbol was created to serve as the place holder. Some old European systems seem to have used a dot or a decimal point. It was Indian thinkers who were the first to acknowledge that this break was not just a blank space, but an actual number.
History tends to gloss over this invention in favor of more provocative mathematic discoveries such as algebra and calculus. Yet, few of these advances would be possible without the number zero. When you think about it, the understanding of zero as a number is a real human achievement.
Steven Glicksman, FCAS, MAAA, is an actuary with Glicksman Consulting, LLC in Boca Raton, Florida. His son, Paul Glicksman, is a technician with the firm.