Zero the Hero
By: Apoorva Panidapu
Tags: History Of Mathematics, Mathematics, STEM, History, Mathematics Education

Gems in STEM: The History of Zero

Hi everyone! Quick recap: this bi-weekly column, Gems in STEM, is a place to learn about various STEM topics that I find exciting, and that I hope will excite you too. This column will always be written to be fairly accessible, so you don’t have to worry about not having background knowledge.

Now, what are we going to talk about today? Nothing!

Okay, okay, today we’ll be briefly discussing the fascinating history of the number zero. Now, using the term “number” is a little presumptuous, because it first came into play as a placeholder.

In particular, the first known appearance of this idea of zero was in Mesopotamia, around 5,000 years ago. The Sumerians used a counting system for practicality — to count their goods and to keep track of things like wild horses and cattle. In writing, scribes used spaces to denote the absence of a number in a place (hence the term placeholder). Naturally, this idea found its way into to the Babylonian empire around 4,000 years ago, and they were the first to really use a symbol (instead of a space) to indicate this absence. Their symbol looked like this:

To illustrate what I mean by a placeholder: the number 808 means we have no tens, i.e. there is an absence of tens. But at this point, zero was just a symbol — the Sumerians and Babylonians didn’t know how to perform operations with it.

Independently, the Mayans also coined a symbol for zero around 350 A.D, using it as a placeholder in their (very complex) calendar systems. Similar to the Babylonians, they never used it with operations or calculations. Their zero looked like this:

And now, the big moment when zero transforms from a sidekick (a placeholder) to a hero (a number)!

This change took place in India, where zero (“shunya” in Sanskrit) became a mathematical concept. The concept of zero first appeared around 458 AD. The first example of a written zero was found in India, carved on the side of a temple wall. It dates back to the ninth century, and was thought to be the earliest record. However, researchers later recovered an ancient record called the Bakhshali Manuscript, which scientists also thought came from the ninth century. But, via carbon dating, it was discovered that it was likely written as early as the third or fourth century, making it the new earliest record of zero as a number! The Indian number system evolved into the one we use today, as they used nine number symbols with zero denoted as a dot. In 628 AD, Indian mathematician Brahmagupta was the first to formalize operations using zero, as he quantified it in addition and subtraction. He attempted to also formalize zero in division, but had a hard time with this problem (which will be addressed later).

As mathematics flourished and developed, these ideas started making their way eastwards to China, and westwards to Islamic and Arabic cultures. Zero journeyed with Arabian voyagers and arrived at Baghdad in 773 AD. The Arabian mathematicians started to base their number system on India’s system, and started working their own magic with zero.

In fact, in the ninth century, polymath Mohammed ibn-Musa al-Khowarizmi was the first to develop the beginnings of algebra, solving equations equal to zero. He called zero “sifr,” which the word “cipher” is derived from. By 879 AD, the symbol for zero started to look like how we write it today — as an oval, rather than a dot. (But, at this point it was smaller than the other numbers.)

At first, the idea of zero was viewed as a villain instead of a hero in Europe. In particular, the Roman Empire’s established number system opposed the Hindu-Arabic system. But, in the 13th century, European mathematicians like Fibonacci celebrated zero (the hero) by using it in their works, in turn advocating for this new number system. Thus, zero joined forces with Europe’s mathematics, too!

In the following centuries, mathematics evolved from no longer being solely about practicality, but to a beautiful world of abstract concepts and beautiful structures. In this evolution, zero has continued to be a mathematical wonder. Yet, the problem of division by zero confounded many. Working with this problem formed the cornerstone of calculus. Calculus would allow anyone to break systems into smaller and smaller units that approach zero, meaning we wouldn’t have to divide by 0. (Interestingly enough, researchers found earlier signs of calculus in India before Leibniz and Newton’s works, likely a result of India being the first to champion zero as a number!)

Nowadays, it’s hard to imagine our lives without our hero, zero. It’s something schools take for granted to explain we have nothing of something. It helped create the foundation of computer programming — the binary number system. It plays an integral role in physics, economics, and so many other fields. So it seems that something can indeed come from nothing. All hail zero the hero!

To end this, I want to give you a pick-up line that will definitely work on anyone:

Are you the number zero? Because I can’t imagine my life without you. <3

If you do (somehow) end up with nada, zilch, zero results from this line, remember nothing is still…something?

Until next time! If you found this interesting, make sure to check out the next column! Again, if you have any questions or comments, please email me at apoorvapwrites@gmail.com.