As far as numbers go, zero has throughout history caused mathematicians no end of grief and discomfort, yet it remains an important chapter in mathematical history.
Zero was one of the last numbers to gain universal acceptance by mathematicians.
In today’s world, zero would be one of the more difficult numbers to live without, even though by its very nature it is difficult to say whether or not it is even a real number.
Indeed, apart from such mathematical abnormalities as “imaginary” numbers and the like, it seems that the last number accepted universally by mathematicians is that magic number of zero.
The Ancient History of Zero
In reality, the number zero hadn’t been accepted into any known mathematical system of numerals until sometime in the 9th century A.D., and the best evidence is that it first became fully recognized as a numeral in India. A few centuries prior to this time the Romans had found a way to recognize nothing in their Roman Numeral system, but instead of receiving its own symbol, it was denoted by a word – nulla (meaning “nothing”). Prior to this time, different cultures with different mathematical traditions had found any number of different “tricks” to enable them to represent the absence of numbers, though none had accepted zero as a number in itself.
It would be still another several hundred years after the arrival of zero in India before it began to catch on amongst mathematicians (though it can be very difficult to trace something as obscure as the use of a number through history, so there is some fog which still needs to be cleared away in this area). One thing that is clear, however, is that the process the world went through in order to achieve a basic ten-digit set of numerals, out of which could be constructed any other number imaginable, was one which spanned both millennia and continents.
But if one stops to truly think about the difficulties involved in this number, it begins to make some sense why it wasn’t accepted before this.
What is Nothing?
After all, even looking at it from a modern perspective, should zero be considered a number? Sure it is beneficial in mathematical equations as they are known today. It would certainly be difficult to write the number 10 without it. Or 100 for that matter. But ancient mathematicians seemed to be getting along just fine writing numbers like that before zero came along, when they used different symbols and place holders that represented the idea of nothingness.
That's all zero is, after all. Just a symbol of something that doesn't exist. And in this sense, it truly isn’t a number at all, but rather a symbol of an idea, rather than something truly quantifiable.
The number zero is a good stepping stone into understanding the basic concepts behind the math of such ancient thinkers as Euclid and Pythagoras. While their mathematics were surely impressive (especially for their time), they held a different purpose and meaning than they do today.
To these ancient scholars, mathematics tended toward very practical applications – how to find the area of a triangle, how to determine pi, how to use geometric proofs to find unknown quantities. These were elements of mathematics that can be used in architecture, engineering, accounting, and many other applications, but never in such matters, where actual, physical things are being measured and counted, would one find the need to quantify nothingness. After all, if an engineer is designing a building and ends up with a length of zero, chances are good that there is something wrong with a measurement somewhere.
This being said, the very idea of zero being considered a number sent the ancient Greeks into a fit of philosophical (and even religious) arguments and disputes over what exactly constitutes a number, and whether numerical status can really be applied to a representation of nothingness.
The establishment of zero opened the door to all sorts of mathematical strangeness – negative numbers, irrational numbers, decimals and imaginary numbers, all of which certain mathematicians (specifically Pythagoras) railed harshly against.
The Importance of Zero
With the advent of Arabic numerals (the forerunners of the standard numerals today), zero became a necessity, especially in a base-ten system where multiples of ten are denoted by the addition of a zero (this is the most common system in today’s world). The number zero as a standalone entity truly became important with the advent of algebra, for often times in solving an algebraic equation, the number zero becomes a crucial element by itself, while still retaining its basic meaning – the representation of nothing.
In truth, the idea of zero doesn’t seem quite so daunting until one truly attempts to wrap their brain around what it truly means, and why it is mathematically necessary. At that point it becomes a journey into the very heart and soul of mathematical philosophy.
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