Sunday, June 26, 2016

Blog Post 6: History of Zero

Zero is a unique and central role in mathematics. In math 310 for example, the zero element of each ring,or the additive identity, is what helps determine if a set is or is not a ring. When added to itself or another number, the number does not change. Also when multiplied by any number, that number becomes zero. It is also a placeholder in many number systems. In fact, most ancient civilizations had some sort of characteristic that represented a zero in their numeral systems.

The Babylonians originally did not have a symbol for zero, therefore their notation is hard to interpret. Today, for example, we would find it difficult to tell the difference between 14, 104, and 1,004 without the place holder of zero. Instead the Babylonians left a space in the middle of numbers or at the end to distinguish the zero place holder. Thus, to us who are not use to reading Babylonian numerals, determining place value is difficult. Eventually however, they did come up with a symbol that represented the space between the number, yet they did not have a concept of zero as an actual number.

Around 650 zero became common in Indian mathematics. Mathematicians such as Brahmagupta, Mahavira, and Bhaskara used zero in mathematical operations. Brahmagupta, for example, explained that zero subtracted from itself is zero and zero multiplied by any number is zero. His only mistake was that of dividing by zero. The Bakshali manuscript may be the first document to ever have zero used in a mathematical purpose.  Around 665 the Mayans also developed the number zero. However, it was more isolated where as the Indian concept of zero spread to surrounding civilizations such as the Arabs, Europeans, and Chinese.

Mayans used a base 20 numeral system. They however had three symbols, a shell shape, that represented zero, a dot, representing one, and a stick representing five. They used zero as a place holder. For example in the number 402, they would have 4 dots in the 100's place, a shell in the 10's place, and 2 dots in the one's place. They often used zero when it came to keeping track on their Long Count calendars. 

The Chinese were estimated to begin the use of zero as a place holder somewhere between the 1st and 5th century. They used counting rods for calculations and according to A History of Mathematics, the rods "gave a decimal representation of a number, with an empty space denoting zero." Zero was treated similarly to the way the Babylonians treated zero. It was more of place holder, unlike the Indians who developed the numerical zero. The oldest surviving mathematical text from the Chinese containing a symbol of zero was the was from 1247, the Mathematical Treatise in Nine Sections.

In 773, zero had reached the Middle East. The first to work on equations with zero was the famous mathematician Al-Khowarizmi. He worked on equations that equaled zero, where algebra was invented. By 879 zero was written very similar to how we do now of days, an oval shape, however, he wrote it smaller than the other numbers.

The Europeans, in the 11th century, began to use zero in operations such as addition and multiplication. Voyagers from Arabia were the first to bring texts of Brahmagupts and his colleagues. Fibonacci built on Al-Khowarizmi work in his book Liber Abaci. Fibonacci's developments with zer quickly spread via Italian merchants and German Bankers. Accountants were able to determine when the books were balanced based on when the positive and negative amounts were equal to zero.  In the 13th century, manuals of calculation, such as multiplying, adding, and extracting roots, became common in Europe.

Hossein Arsham, a mathematician at the University of Baltimore, writes, "The introduction of zero into the decimal system in the thirteenth century was the most significant achievement in the development of a number system, in which calculation with large numbers became feasible. Without the notion of zero, the modeling process in commerce, astronomy, physics, chemistry, and industry would have been unthinkable. the lack of such a symbol is one of the serious drawbacks in the Roman numeral system."

Adding, subtracting, and multiplying by zero are now relatively common operations. Zero was not always agreed on and confused many great minds. The concept was not always concievable. Many though why do we need a symbol to represnt nothing. However, in the day and age we are in now, zero is just as common as any other integer. Developing zero has been one of man kinds most significant accomplishments.

Work Cited


  1. Lots of good history here.

    Complete: to be an exemplar it could use more stuff/time shown. More about place value, a look at the Babylonian or Mayan numbers. You might be conflating a bit the two separate issues of place value and the question is nothing a number. Leonardo of Pisa could get name-dropped in the European section. What are the important properties of zero - can you make some ring/Math 310 connections?


  2. Hey Anthony,
    This is some neat history on Zero. I still think its is crazy that so many people didn't accept zero so long ago.
    It would be cool to see some work on zero that you have done or something that you think is awesome about zero.

  3. It is really hard to try and realize a mathematical universe without zero, and I think that most of us that study today, take many things for granted. It is obvious that many of these things, like the number zero, took hundreds, if not thousands of years, for mankind to try and get a grasp on. Something that would have been kind of neat to view would be the struggles these groups of people with accepting zero. Is there a particular reason/reasons that some cultures were embraced Zero more so than others?
    Thanks for sharing Anthony!

  4. Anthony,
    I am fascinated by this topic. How crazy is it to think, today, of a world in which zero does not exist, or at least is not used in mathematics! It certainly would make division by a variable easier, no restrictions on what that variable could be. I appreciate your post and especially like how you highlighted the difference between zero as a place holder and zero as a number with properties.

    Yet, the great part about realizing that zero was invented is that you then get a glimpse into how math goes from an idea to a part of our daily lives. I sort of imagine that mathematicians of the day started to get frustrated with the difficulty of writing numbers without the place holder, so they stuck one in. After some time, someone thought, so, I can use all of these other numbers in math, why can’t I use this place holder as well? Then, “Okay, if I am going to use it, what properties will it have? What will happen if I use it in multiplication, division, addition, subtraction?” Voila, someone sets down the rules and we now have this amazingly useful place holder!

    By the way, I did find one typo. You say, “thirteenth century was the msot significant achievement” and is should be “thirteenth century was the most significant achievement”.

    Thank you for your post,

  5. Anthony this was a great post on zero. zero is such a weird number and its so interesting on how it wasnt even considered a number back in the day. Seeing how different numbers are now with and without zero is crazy because without zeros its a completley different number to us now. great job!!!

    -Brianna Podsaid