than meets the eye. Without the concept of zero, math as we know it would be far less

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1 History of Math Essay 1 Kimberly Hannusch The Origin of Zero Many people don t think twice about the number zero. It s just nothing, after all. Isn t it? Though the simplest numerical value of zero may be just nothing, it has much more significance than meets the eye. Without the concept of zero, math as we know it would be far less advanced, not to mention that half of a computer s language alphabet is made up of zeros. So where does the significance of zero lie? Let s take a look into the original development of the number to find out. There are many ancient cultures whose number systems did not include the concept of zero. For example, the Egyptians never dealt with zero, nor did they have a symbol to represent it. Their math mostly dealt with geometry and measurement in order to plot out the size of the land left after the yearly flooding of the Nile. There was no use for zero in that context, and since necessity is the mother of invention, they did not bother to make up a symbol for the concept of nothing. Not even the Greeks, who prided themselves on their logic and mathematical prowess, could come up with the concept of zero. Again, they dealt with a lot of abstract geometry, using drawn figures instead of lots of numbers. Their superstitious fear of any numbers that were not whole numbers probably contributed to their avoidance of delving into the concept of nothingness. If they could not accept irrational numbers, how would they come with a number that represented absolutely nothing?

2 The Babylonians were the first people to use zero as a placeholder around 300 B.C. 1 To be clear, the first occurrence of the concept of zero was not as a digit which represented nothingness. Instead, it was used solely as a placeholder in order to distinguish numbers such as 65 and 605. The placeholder zeroes would tell if the scribe meant 6 ones or 6 tens. This system was less confusing than just leaving a space there or trying to find out by context, which is what had been done up until that point, as far as experts can tell. The Babylonian zero was marked as two angled wedges, such as the figures in the picture to the right. Though they correctly used zero as a placeholder, they never connected it with the concept of nothingness and they never developed it into a number on its own. The Mayans were another culture which developed the placeholder concept for zero completely independently, though they were about 300 years later than the Babylonians. Their zero emerged around 36 B.C. The Mayans were interested in astronomy and made very accurate solar and lunar calendars. This math required very large numbers in their vigesimal (base twenty) number system, so they needed the zeros in order to have accurate calculations. Remarkably, they came up with some of the most accurate calculations of ancient times for the length of a solar year and a lunar month. For the solar year, they calculated a length of days, with an amazingly small error of only percent compared to our modern measurements. For the lunar month, they calculated a length of days. This had another extraordinary error of merely percent compared to our modern measurements. Their 1 Some scholars say that there was a precursor to this zero with the Sumerians around 2000 B.C., but it is not totally agreed upon. Regardless, the Sumerians passed down their number system to the Babylonians who have the first non-contested version of a placeholder zero.

3 calculations for the year and month were more accurate than the European ones at the time. However, their zero only functioned as a placeholder even through the peak of their culture from 250 through 900 A.D. It wouldn t be until the 7 th century that the concept of zero as a number presented itself. Some scholars say that the Babylonian placeholder concept for zero wound its way through the years and cultures down to the Indians, and that they took it and developed it into the number zero. Others claim they developed zero independently. Regardless, India is the first place that we see zero as a separate number which represents nothingness. The Hindus were also great astronomers, and, like the Mayans, needed a system to deal with very large numbers. They used the placeholder concept of zero for these large numbers for a very long time. However, their religious culture also included an emphasis on emptying oneself and grasping at nothingness. At some point, this religious idea of nothingness collided with astronomical mathematics and zero as we know it was born. As early as 458 A.D., we see different words used to symbolize zero such as void and space. Then, finally, in 628 A.D., we see a symbol being used for zero as a digit rather than a mark between numbers to indicate places. This zero showed up in a work by Brahmagupta, a Hindu astronomer and mathematician. The symbol that he used was a dot below other numbers. Brahmagupta s work, called Brahmasputhasiddhanta, not only used zero as a digit, but it also outlined the rules for reaching zero through addition and subtraction and for adding, subtracting, multiplying, and dividing by zero. The only concept that he got wrong was the rule for dividing by zero, which would continue to stump people until Newton and Leibniz independently invented calculus in

4 the 17 th century. With the introduction of the full concept of zero, other doors were opened as well. Brahmagupta s writing also included negative numbers and explored irrationals. From India, the concept of zero spread to other cultures. Next, zero was most notably developed by the Arabians in Baghdad. It became part of the Arabic number system, and the symbol was the circle shape that we know today, though it was a bit smaller. In the 9 th century, Mohammed ibn-musa Al-Khowarizmi became the first mathematician to solve equations that equaled zero. He was famous for developing algebra, and for creating algorithms (a word which came from a corruption of his name) for multiplying or dividing large or difficult numbers. Finally, with the invasion and conquest of Spain by the Moors, zero was brought into Europe by the middle of the 12 th century. However, it took many years centuries, even for zero to be accepted by the European authorities due to their distrust of Arabian math and the idea of having a symbol which represented nothing. One notable person who supported the use of zero and the amazing ease of Arabian numerals (as opposed to Roman numerals) was Leonardo Fibonacci, an Italian merchant and mathematician who taught the new methods in his book Liber Abaci. Other merchants and accountants agreed with him since it was much easier to balance their books and add and subtract numbers using the new numerals (which are the ones we use today) rather than writing out the hefty Roman numerals. However, the governments and the Christian church at the time had a deep mistrust for anything from the Muslim world, and they argued that a zero could be made to look like a 6 or 9, and a 1 could be changed to a 7. Because of this, zero and the Arabic numerals were banned, though they continued to spread despite all of the disapproval.

5 By the 1600s, zero was more widely used and accepted throughout Europe. Rene Descartes based his coordinate system off of a zero-zero origin. Later on, Newton and Leibniz would contemplate how to divide by zero and would independently invent calculus. None of these developments could have occurred without the number zero available for placeholding and for representing an amount which contains nothing. Neither the insanely accurate calculations of the Mayans, the astronomy of the Hindus, the development of algebra by the Arabs, the more advanced bookkeeping of the Europeans, nor the development of calculus and Cartesian coordinates would have been possible without the existence of a zero symbol and at least some understanding of the existence of nothing. Our math would not be the same as it is today if we didn t have zero.

6 Sources: Aczel, Amir. "The Origin of the Number Zero." Smithsonian. Smithsonian Magazine, Dec Web. 11 June < /?no-ist>. Coates, Alexandre. "On The Origin Of Zero." Mostly Odd. N.p., 02 June Web. 11 June < Mastin, Luke. "Mayan Mathematics." The Story of Mathematics. N.p., 1 Jan Web. 11 June < Matson, John. "The Origin of Zero." The Scientific American. The Scientific American, 21 Aug Web. 11 June <http%3a%2f%2fwww.scientificamerican.com%2farticle%2fhistory-of-zero%2f>. Szalay, Jessie. "Who Invented Zero?" LiveScience. TechMedia Network, 28 June Web. 11 June < Wallin, Nils-Bertil. "The History of Zero." The History Of Zero. Yale Center for the Study of Globalization, 19 Nov Web. 11 June < Picture:

The Emergence of Medieval Mathematics. The Medieval time period, or the Middle Ages as it is also known, is a time period in

The Emergence of Medieval Mathematics The Medieval time period, or the Middle Ages as it is also known, is a time period in history marked by the fall of the Roman civilization in the 5 th century to the