The Number Zero: A Controversial Idea

by Connor Storey

The number zero has been one of the world’s most controversial ideas. Western countries, such as Ancient Greece, rejected this number as it represented nothingness, complete void, and had properties that no other integer had. Today we take the number for granted and we use it in our everyday lives without ever thinking what the number really represents. What really is nothingness? It’s a hard concept to comprehend and has been a challenging question that both philosophers and mathematicians have been faced with.

In our most primitive times zero was believed to be a placeholder, not a number. Number 1 was the first number, followed by two 1’s, then three 1’s etc. It was thought that there was no need for the number zero since we only needed numbers to count. Think of it this way - if you were to count the number of cows on the farm the first number you begin with is one, then two, then three. You don't count zero cows on a farm because if you're counting the number of cows on a farm, you already know that there are some cows there. It’s just a question of whether there is one or many.

As I previously stated, Ancient Greece rejected the idea of zero as it questioned their whole philosophy. In fact, irrational numbers such as √2 and the golden ratio were believed to be numbers before zero was even considered one. The Greek universe was known for their advanced understanding of geometry and using this to understand numbers. One of the challenges faced by zero was that it was the only number that if added to itself it will never change. This challenged a basic principle called the Axiom of Archimedes, which states that any number added to itself will surpass another number. It refuses to make a number greater or smaller by adding or subtracting a number by zero. With multiplication and division, zero becomes even stranger.

Multiplication can be illustrated by using a rectangle. A multiplication of 2 x 5 can be represented ,geometrically, as a rectangle with side lengths 2 and 5 units; the area enclosed is the multiplication between the two. So from this you can show that the area is 10 squared units. Meaning that 2 x 5 = 10. Now what happens if one length is zero, or if both lengths are zero? The outline of the rectangle becomes unclear and an area cannot be calculated so n x 0 = 0 (e.g. 2 x 0 = 0) . Now let's take division. Division is simply the opposite of multiplication. You could view it as undoing a previous multiplication. From the example above you can see that 2 x 0 = 0 so division would assume that (2 x 0)/0 = 2. However, 3 x 0 and 4 x 0 is also equal to 0. This suggests that (2 x 0)/0 = 2, (3 x 0)/0 = 3 and (4 x 0)/0 = 4.  This pattern starts to show a contradiction as you can simplify the following fractions giving 0/0 = 2, 3 and 4. This confused Greek mathematicians because dividing by zero broke the foundations of logic. The Greeks found this number difficult to understand as they based numbers on geometry and couldn’t find a way to geometrically understand nothingness. So out of utter confusion, Ancient Greece rejected it as a number completely and did not accept it until nearly two millennia later.

It was not until the West met Arabic and Hindu mathematics that zero was considered a number. After the collapse of Ancient Rome, Aristotle’s influence was still paramount throughout the West. The Church took Aristotle’s ideas and accepted his reasoning so any questioning of his ideas seemed that Christianity was being attacked and unfortunately, Aristotle was a firm believer that nothingness didn’t exist. However, once the Church had its powers restricted the Renaissance period became a time where new ideas were developed and discovered. Meaning that people could question the whole of Aristotle's philosophy - including the existence of zero. Not until the 12th century was zero considered a number of its own. Without the recognition of the existence of zero, many forms of science wouldn't be possible if it wasn't for the beginning for the controversial idea: zero.