By: Natalie Oulikhanian
Although the number zero is a significant structural component to the numeric systems that we know and use, the creation of a symbol representing nothingness is a relatively new development. The uses that zero has in the modern world are crucial to the exceedingly simple and complex mathematical process that are completed, that it seems impossible for zero to have not always been an integral part of mathematics. It is only until recently that zero overcame its controversial path to being defined as a value in itself. However, the shaky origins of implementing types of numeral systems justify this delay. The simplest of daily activities that required forms of mathematics had never required the consideration of the absence of anything. However, once established, zero’s impact on modern mathematics surpasses these minor processes and can be credited for the influx of complex calculations that have made significant benefits in daily life. To fully understand the colossal impact that this value has, we must look into the sometimes rocky origins of a nothing among the origin of value.
In history, the first ever counting systems are generally similar to the procedures for counting that are still common today. Like the uses that tallying finds its way in modern life, these ancient counting techniques are only compatible with necessary menial activities such as the tracking of time or the recording of certain quantities. These methods had served their basic purposes well only until societies grew larger and much more demanding. Numbers quickly began to play a role in more than just the documentation of quantities but expanded its involvement into processes such as the distribution of materials, calculations required for architecture, or the creation of accurate calendars, all which needed the conveniences which revolutionary mathematical calculations would provide.
Ancient Mesopotamia — circa 3400 BCE — became the first civilization to invent number systems which used mathematical calculations to help solve the growing complexities of their routine activities. Outside of having created a numeric system capable of conducting arithmetic operations, the Babylonians became the first to use a variation of zero that is still present today: the placeholder. Unlike the standard version of a placeholder that is universally common today, Babylonians would only use their digit in medial positions (think of the 0 in 101). This is still significantly different from modern numbers that include zeros on the far-end side of numbers which can be infinitely set next to one another to indicate a larger or smaller number in each repetition. Rather, Babylonians would have unique symbols for each of these numbers that could have used this aspect of a placeholder.
Although other civilizations, such as the Mayans or Greeks, had numeric systems that included their own versions of zero similar to the Babylonians, its function still remained as a placeholder until seventh century India. Mathematician and revolutionary thinker, Brahmagupta shaped modern mathematics forever by applying the concept of nothingness, which is rooted deeply in Indian culture, into a symbol that can represent the concept in a mathematical lens. Through his work, Brahmagupta provided rules and direction to computing with zero, such as division, by treating the symbol as a number by itself. It is difficult to imagine the process of long addition without zero as a key component in numbers themselves.
As the value made its journey across the globe, the concept significantly influenced mathematicians in the Middle East and would soon lead to an essential component in the Arabic number systems. However, zero would also have its own fair share of challenges before its breakthrough in the mathematical branch of calculus which highlights zero’s most colossal achievements. Zero’s roots in spirituality made the value have a struggling path to become the digit that is so commonly used and praised today. In 1299, the digit was banned in Florence along with other Arabic numbers as they were perceived to encourage fraud and elements of evil. This is significantly a reflection of the negative views that are associated with “nothingness”. For example, the placeholder use of zero was especially turned down as the addition of extra zeros to the end of a number was interpreted to allow for the inflation of prices. Zero also faced criticism for being a value that offers the possibility of negative numbers, and therefore the legitimization of debt.
The passion for knowledge and answers during the renaissance had saved the zero of its misadventures. Thinkers became dedicated to considering the otherwise concealed questions relating to zero such as its division and its uses. Soon, the digit found itself as a remarkable component to the cartesian plane: the origin (0,0.) Renaissance thinkers and mathematicians were enthralled with zero’s ability to increase and decrease numbers infinitely depending on its placement and led to the development of the most, if not the most, important and influential branches of mathematics: the study of continuous change, or calculus. In calculus, any changing rate can be graphed through slope functions, and no matter how varying the slope may be, once zoomed in enough, the perceived curves begin to look more like straight lines — and soon, small chunks representing the size of zero.
Nothing matters. Zero’s difficult path towards recognition fostered some of the most influential advancements in modern mathematics. From all over history and the globe, the variable uses of zero have permanently simplified and changed operations in algebra and have sparked the creation of calculus. The once resented number became a powerful tool to help describe the rate of anything’s change in the world — from the stock market or to the building of infrastructure — the development of effective technology has only increased. Zero, much like mathematics as a whole, came from humble beginnings. But its inclusion as a positional number in history has unleashed the sophistication in mathematics' brilliant applications today.
What Did You Learn?
Q: What makes zero such an important digit in mathematics?
A: Zero has two fundamental roles in math: a digit acting as a placeholder and a number to represent the absence of value. In the first, zero constitutes for nothing in a certain place value which reduces the need to create a unique symbol for every number possible. This simple replacement drastically eases the complications that can arise from basic mathematical operations such as long division. In the same way, the digit zero can be infinitely placed next to one another to either create a number which increases or decreases in value (0.001 to 0.0001 or 100 to 1000.) In its second use, the representation of nothing as a number itself, zero is a crucial part to understanding mathematical operations in algebra, algorithms, and its remarkable use in calculus since it legitimizes every other number as being relative to zero. This makes it able to calculate the rate of change, make predictions, and has even found its use in the binary system.
Q: Why did zero become recognized as a number so late?
A: Zero, much like the rest of mathematics, originated from the practical applications at the time. When ancient civilizations only required math for applications such as simple trade or architecture, there was no need for something that represents the absence of anything when all activities used the existence of something. After its creation as a placeholder, India found another purpose for zero as a symbol that represents nothing. However, the expansion of this concept was not quick or accepting. Spiritual beliefs and the fear of applications such as fraud, limited zero’s potential in the world. It was only until the renaissance and the era’s influx of questioning and revolutionary thinking that zero would be thoroughly considered as a part of mathematics. This drastic change led mathematics to revolutionize from simple, practical applications, to abstract concepts such as calculus, which can be credited for some of math’s most beneficial uses in the world.
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