Of all the numbers out there, there is something special about zero. We can find real world examples of other numbers, be it $ 1.99 red balloons, 100 years of loneliness, or anything else we'd like to put in a table. But it's hard to find examples of nothing – even the supposed vacuum of space is disturbed weak gusts of hydrogen atoms.
Maybe that's why zero is a fairly recent invention. Although it emerged in various forms in various places, the concept of nothing as number is at most a few thousand years old. And sometimes it doesn't seem to have existed at all. Both the Egyptians and Romans did not seem to use zero.
Yet zero is very important to us today. The concept plays a fundamental role in calculus as we calculate derivatives that converge to zero. It is also used in coordinate systems on graphs, starting at the point (0, 0).
Ancient civilizations also found use in zero, first as part of numerical systems and later as a mathematical tool. The Sumerians are believed to be the first to recognize the idea of nothing (although they did not come up with a symbol for zero until later). Likewise, the Maya independently developed the idea of zero. The concept of nothing later traveled from the Middle East to India, China and elsewhere.
European civilizations were quite late with the nothing game, not incorporating zero into their cultures until after the mathematician Fibonacci brought the Indo-Arabic numeral system to Europe after traveling the Middle East and Africa. There, as elsewhere, zero would prove to be a revolutionary concept, inspiring medieval and Renaissance thinkers to provide fundamental insights into mathematics and the world.
Count to nothing
The discovery of zero does not seem to have come all at once, but rather in stages. Scholars think it started with the concept of nothing as a placeholder during counting. This is how the Babylonians used zeros about 4,000 years ago. When counting, they divided their numbers into columns, just like we do now, a concept called positional notation. For us, the number 115 has three columns of place values: ones, tens, and hundreds. There is a five in the ones column, a 10 in the tens column, and one in the hundreds column. For example, to write 105, we need to show that there is nothing in the tens column, something that was achieved with a zero today.
Although the Babylonians used a different number system from us, they did counted in much the same way using positional notation. When they had to show that there was nothing in a column, the Babylonians came up with the idea of just leaving a space there – nothing in the truest sense of the word. It is our first true example of an acknowledgment of the concept of nothing.
Babylonian Cuneiform Numerals. (Credit: Josell7 / CC BY-SA 4.0 / Wikimedia Commons)
More than 1,000 years later, under the Seleucid Empire, the Babylonians seem to use wedge-shaped characters instead of spaces – some of the first graphical representations of zero. Yet the Babylonians do not seem to have expanded their concept of zero to an actual number. For example, a stone tablet with maths sums will have the calculation "20 – 20", but leave the answer blank – an undefined sum.
The Maya applied zero in much the same way. When writing dates, they needed a way to put a zero in columns where necessary. For example, the date corresponding to the beginning of what they believe to be the current age of the world was written 22.214.171.124.0 in Mayan notation and corresponded to 3114 BC. Since the Maya had no contact with Eurasia until long after these signs were written, it is clear that the Maya independently invented the concept of zero.
Mayan Numerals. (Credit: Original: Neuromancer2K4Vector: Bryan Derksen / CC BY-SA 3.0 / Wikimedia Commons)
The Maya seem to have used different symbols for zero, although a scale was the most common. The shell glyph also appears to have been used to denote the concept of nothing more broadly. A translated verse in the Mayan text mourning a fallen leader reads, in part, "no pyramid, no altar, no earth / cave." The same shell glyph that represents zero in their number system appears here in a more abstract sense and means nothing.
Zero in motion
From Babylon, zero slowly began to spread to other parts of the world. It emerges in Greece around the fourth century BC, probably brought back by Alexander the Great after he conquered the Babylonian Empire in 331 BC. Here we begin to see traces of the modern oval that we use today to represent zero. Greek astronomers such as Ptolemy used a hollow circle when calculating trigonometric figures, often adding a dash or line across the top. This, Robert Kaplan argues in his book The Nothing That Is: A Natural History of Zero, indicates that they probably thought zero as something closer to a punctuation mark between real numbers, rather than a number in itself.
For a true appreciation of the position of zero on the number line, we have to venture to India. There, researchers see that the first solid proof of zero, called "sunya" by the Indians, is used in mathematical calculations. It is a sign that mathematicians there understand zero as a unique numeric entity. Probably the first to make this logical leap was a man named Brahmagupta, a fundamental figure in Indian mathematics. In his Mathematical Treatise Brahmasphutasiddhantawritten in AD 628, Brahmagupta provides rules for doing zero calculations that reflect what we understand today.
When zero is added to or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero, ”he writes.
This is a logical leap, argues neuroscientist Andreas Nieder in one 2016 paper.
“For a brain that has evolved to process sensory stimuli (something), conceiving empty sets (nothing) as a meaningful category requires high-level abstraction. It requires the ability to represent a concept that goes beyond what is perceived, ”he writes.
Khmer ciphers from Sambor inscriptions dated to A.D. 683, found in present-day Cambodia. Some say this numbering system includes the earliest usage of zero. (Credit: Paxse / CC BY-SA 3.0 / Wikimedia Commons)
The true origin of zero is still a matter of debate among historians and mathematicians. For example, the number zero may have surfaced even earlier in what is now Cambodia than in India, says Amir Aczel. The mathematician undertook years of searching for the origin of zero and ended up in a barn near the ancient city of Angkor Wat. There carries a tablet dating back to the seventh century AD, which he says is the first true zero. While he writes Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers, that would move the first true zero from India to Cambodia, extending our timeline of the number by about 200 years.
Where it was first discovered, our current zero – the one we write with a hollow oval – didn't make it to the Western world until the 13th century. That's when Fibonacci, nowadays is best known for one eponymous number sequence, Europe introduced in its text to the Indo-Arabic zero Liber Abaci. The book, published in 1202, brought our modern number system to the continent, including its fundamental zero. The numbers caught on and mathematicians carried the zero to the Renaissance and beyond.
In Europe, like everywhere zero was discovered or introduced, it seems that the number has never gone out of style. Once nothing shows up, it's there to stay.