Observing whether something was present or not, and if present, how much or how many there were, has been the primary means to adapt and survive for humans, from hunter-gatherers in constant search for food and safety to early city dwellers advancing in agriculture and trade. Many thousands of years later today, it’s still the same instinctive and inherent counting concept that moves mankind forward in attempts to understand nature and the further universe around us. Only now after it has evolved and ramified into much more sophisticated fields of analysis and interpretation, we can call it ‘mathematics’. 

 

Looking back in history, one of the most notable leaps in human mathematical cognition seems to be the emergence of ‘zero’ as a concept and symbol of its own. The first recorded signs of zero date back to 4000 BC, where spaces were used to show absences in number columns on Ancient Sumerian scribes. Babylonians used zero as a placeholder or as a tool to differentiate ten from hundred or thousand. Mayans also used zero for their calendars. However, it was only in 7th century India that zero was not just as a placeholder but also recognized as a number with a symbol of its own. The Hindu astronomer and mathematician Brahmagupta considered zero as a null value referred to as “sunya”. He also defined the fundamental characteristics of zero in arithmetic that “When zero is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero.”

Building on this, in the 9th century, the Persian mathematician Mohammed ibn-Musa al-Khowarizmi, studied equations that were equivalent to zero, hence, laying out the foundations of algebra. As zero spread to Middle East and thereon to Europe by 17th century, it fueled breakthrough inventions in mathematical modeling, like Descartes’ Cartesian coordinate system or the advent of the field of calculus, hence, unlocking the way to grasp highly abstract mathematics and also leading the way to the binary architecture of computer science which gave birth to our current day digital technology. 

 

Although zero is such a powerful concept, it is still surrounded by mysteries as it defies some standard definitions in mathematics. For example, is it an even number or an odd number? Is it positive or negative? Is it an integer or not? And it gets weirder when zero becomes an exponent and factorial of its own. We probably all know that x0=1. To explain this, we can look at a simple relationship of exponents such as 23=8,  2(3-1)=23÷2=4, 2(2-1)=22÷2=2, 2(1-1)=20=21÷2=1. Hence, we can deduce that 20=1 and likewise x0=1 , unless of course x is zero. We know that  02=0×0 and 01=0 but what about 00? Is zero multiplied zero-times by itself 0 or 1? Well, that’s why it is ‘undefined’. Likewise, the factorial of 0 equals to 1 is another peculiarity of zero. Since a factorial of a number is the product of that number and the previous positive ones. Because zero is not positive, it is not easy to identify the answer of 0!. However, we can refer to the pattern of 4! = 5!/5, 3!=4!/4, 2!=3!/3, 1!=2!/2, 0!=1!/1 and from this we deduce that 0!=1. Straightforward or odd, what do you think?

 

It is normal to feel challenged by such a hard and abstract concept like zero. In our daily lives it’s a symbol for non-existence or nothingness. Perhaps the most peculiar aspect of zero is how much it allowed humans to build upon, creating a gigantic depth of interpretation, despite being a symbol to represent nothing or none. As immaculately pinned down by Kurt Vonnegut, “Everything is nothing with a twist.”.