This document is a term paper submitted by Zulfikar Pasha Dipto on the mystery of zero. It includes an acknowledgement, abstract, table of contents, and introduction section. The acknowledgement thanks various individuals for their support and guidance. The abstract provides a brief overview of the history and development of zero in different cultures from 700 BC to 1600 AD. The introduction discusses how zero was originally viewed as an empty space rather than a number, and how its usage and acceptance evolved over time in cultures like the Babylonians, Greeks, Indians, and others.

1. Term paper
On
Themystery of
Submitted by….
Zulfikar Pasha Dipto
B3160B024
Submitted to….
Abul Kalam Azad
Assistant professor

2. Date of Submission:March 7,2016
ACKNOWLEDGEMENT
The most pleasant part of submitting the report is to get opportunity.I would
like to thank those who have contributed to it a lot.Unfortunately,thelist of
expression of thanks-no matter how extensive is always imcomplete &
inadequate.This acknoweledgements are no exception.First,Iwould thank
almighty Allah for bestowing us the patience & courage to finish this huge
task within deadline.
In addition,I sincerely acknowledge my debt to Mr. Abul Kalam Azad
,honourable faculty,AIBA for his valuable counseling towards the
improvement of the report.Without his encouragement,this would have never
been possible.
At last,I would like to convey my gratitude to our honourable senior,Akib
Hasan Srabon,BBA-1,for helping us by giving advice.

3. (i)
ABSTRACT
Zero was not considered as a number.It was nothing but the idea ofempty space.Babylonians
around 700 BC used two hooks to denote an empty space in positional notation.Records showthat
the ancient Greek seemed unsure about the status ofzero as a number and not merely a symbol for
separation is attributed to India.But by the 9th
century AD practical calculations were carried out
using zero which was treated like any other number,even in case ofdivision.It was only around
1600 that zero began to come into widespread use.
And day by day,it became more popular among “Babylonian”, “Roman”, “Mayan” , “Indian”.
Each of them use this number,in different form.Some of them use it as a dot,sometimesit looks like
a symbol or mark etc.

4. (ii)
Table of Contents
Page no.
1. Acknowledgement i
2. Abstract ii
3. Table of Contents iii
4. Introduction 1
5. Rational of the study 2
6. Objectives 3
7. Methodology 4
8. Numerical Calculation 5
9. Graphical Representation 6
10. Result 8
11. Discussion 9
12. Conclusion 11
13. Reference 15

5. (iii)
Introduction
“In the history of culture,the discovery of zero will always stand out as
one of the greatest single achievements of the greatest single
achievements of the human achievement”
-TobiasDanzig
Existence
Zero was not considered a number.There was the idea of empty space,which may be thought
conceptually similar to zero.Babylonians around 700 BC used two hooks to denote an empty
space in positional notation.Records show that the ancient Greek seemed unsure about the
status of zero as a number and not merely a symbol for separation is attributed to India where
by the 9th
century AD practical calculations were carried out using zero which was treated like
any other number,even in case of division.The concept of zero took some time for acceptance.It
was only around 1600 that zero began to come into widespread use after encountering a lot of
support and criticism from mathematicians from the world.

6. (1)
Rational of The Study
Zero is one of the most used term in mathematics.So,we have to know about it’s history
& details,so that we can know about how does it come in the number system.
Brief History
 The Maya civilization (2000 B.C-900 A.D) in the what is now Mexico used the concept of
zero as a PLACEHOLDER:that is,705 is a way bigger number than 75.(like using
comma in written language.)The Babylonians used it similarly in the 7th
century B.C.
 The 7th
century Indian mathematician Brahma Gupta treated zero as a “number” and not
just as a place-holder.He elaborated the rules mentioned on page 2 of his presentation.
 The Hindu-Arabic numbering system that included zero in the way that was used in the
west by Leonardo of Pisa- Fibonacci- in his book of counting,published in 1202.
 Zero gained a central place in the number system soon afterwards,with it literally
separating the positive numbers from the negative ones as in the number line.
 In the decimal system,zero serves as a place holder which enables us to use both huge
numbers and microscopic figures.
 Hence the sheer beauty and usefulness of zero could lend its use to science in its
wonderfully succinct scientific notation.

7. (2)
Objectives
The main objective is to gather knowledge about the invention and theory of
the mystery of ZERO (0). Zero remains as a mystery to us.It is a common
matter of curiosity & thinking about it’s origin.As we can see that it becomes
popular since the pre-historic times.Through the research,we can understand
its method, its usage, calculation procedures, result and conclusion. We will
also gain knowledge about its importance and essence.It will help us to
make the proper use in our practical life.

8. (3)
Methodology
It is a qualitative research .This research work is done by collecting
various data through internet. The link of those useful sites are given
below:-
1) http://www.slideshare.net/DivyaRajput6/history-of-zero-
mathematics?qid=5c61237a-f10c-4788-868c-
62fd4ad7c3a8&v=&b=&from_search=1
2) http://www.slideshare.net/lsccyfairall/history-and-mystery-of-
zero?qid=9637ca07-a246-4ee6-b8cb-349765a9ac1a&v=&b=&from_search=1
3) http://www.slideshare.net/Timmy58/zero-34642070?qid=9637ca07-a246-4ee6-
b8cb-349765a9ac1a&v=&b=&from_search=5

9. (4)
Numerical Calculation
There is a close link between numerical notation and writing systems. In fact, the first
forms of notation were numerical and it took the form of tallies which is represented by
bones. This might explain the fact that in the Semitic languages the words "scribe" and
"count" represents the similar meaning, i.e., SPR. Writing and the notation for abstract
numbers emerged in Sumer at precisely the same moment in history.
In the ancient alphabetic scripts, Semitic and Greek, for example, the letters of the
alphabet were also used to represent numbers. The first ten letters represented one
through ten respectively. The next nine letters represented 20, 30, and up to 100.
The Romans also developed a number system using the letters of the alphabet, but in a
more abstract manner. A much smaller number of letters was needed, namely, I, V, X,
L, C, D, and M. The system was also more abstract because the numerical values
depended to some extent on the placement of the signs. For example IV = 4 whereas VI
= 6. There is no zero element in this system and numerical calculations are extremely
clumsy.

10. (5)
Graphical representation
1) Zero in Mayans:
Six hundred years later and 12,000 miles from Babylon, the Mayans developed zero
as a placeholder around A.D. 350 and used it to denote a placeholder in their
elaborate calendar systems. Despite being highly skilled mathematicians, the
Mayans never used zero in equations . The symbol for 0 in the Mayans looks like a
bowl or an eye. Their numeral system was 20.They used 0 to represent 20.
2) Zero in Babylon:
The Babylonians got their number system from the Sumerians.They are the first
people in the world to develop a counting system. They created 0 in the third
century B.C. The Babylonians were the first culture to invent the place value
system. The Babylonian placeholder was not a true zero because it was not used
alone. Even it wasn’t used at the end of a number. They had a sexigesimal
number system, in which, they counted in 60s, as we count in tens. They never
developed the idea of zero as a number. This is their numeral system.

11. (6)
3) Zero in India:
The number 0 appear in the late 10th century in India. The concept of zero as a
number and not merely a symbol for separation is attributed to India, where, by
the 9th century CE, practical calculations were carried out using zero, which was
treated like any other number, even in case of division .The word for zero in
Hindu-India is “shunya” meaning void or empty. India is recognized with great
respect for its invention of Zero by importance with Technological world .These
are the numbers that the Hindus and the Arabic use.

12. (7)
Result
The calculations consisting long division or fractions become more
complicated with Roman numerals. The advantages with Hindu-Arabic
numbers are obvious.
Arabic numerals are obviously the most abstract numerical notation.
On the other hand,the alphabet is the most abstract form of writing. It
is ironic that the alphabet achieves its abstraction through
phonetization whereas the Arabic numerals are logograms or
ideograms that represent ten numerical values including zero. The
letters of the alphabet and the Arabic numerals, however, share four
important features that enable them to act abstractly:
Each number system contains some elements; twenty-six letters (for
the English alphabet) and ten numerals. Both systems form a complete
set. The total set of possible spoken words can be represented
alphabetically and any number, no matter how large it will be, can be
represented in terms of some combination of the ten numerals 0
through 9.The individual elements of the two systems, the letters and
the numerals, are atomic. That is, they are identical and
repeatable.And finally, the sound or numerical values of the aggregate
elements (the words or numbers) of the system depend not only on the
letters and numerals of which they are made up but also on their

13. order. In other words, both the letters and their order determine a
word and both the numerals and their order determine a number. For
example TOP is not the same as POT. Similarly,24 & 42 aren’t the
same thing.
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14. Discussion
So, as we can see,the development of the place number system
depended on the invention of the concept of zero, an idea that seems
extremely simple and yet is quite sophisticated. For this reason, the
discovery of the concept of zero is often taken for granted. Many
assume that the Greeks, the originators of formal geometry and logic,
made use of it. We are taught about zero in elementary school,
geometry in high school, and logic in college. Therefore, many people
believe logic and geometry are mathematically more sophisticated
than the concept of zero. This is not true and is an example of the
distortion of the history of science effected by textbooks and school
curricula, as pointed out by Kuhn (1972). The Greeks never developed
the operational notion of zero, yet their achievements in geometry and
logic were unparalleled. But as a result of not having a concept of
zero, their arithmetic calculations were laborious and their
development of algebra was stunted.
Hindu mathematicians invented zero more than 2,000 years ago. Their
discovery led them to positional numbers, simpler arithmetic
calculations, negative numbers, algebra with a symbolic notation, as
well as the notions of infinitesimals, infinity, fractions, and irrational
numbers.
The historians of mathematics have always been wondered that the
germinal idea of zero was a discovery of the Hindus and not the
Greeks. Laplace, A great mathematician of the 18th century, wrote:
"It is India that gave us the fabulous method of expressing all numbers
by means of ten symbols, each symbol receiving a value of position as
well as an absolute value, a profound and important idea which
appears so simple to us now that we ignore its true merit. But its very
simplicity and the great ease which it has lent to all computations put
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15. our arithmetic into the first rank of useful inventions, and we shall
remember that it escaped the genius of Archimedes and Apollonius,
two of the great men produced by antiquity" (Dantzig 1954, pp. 19-20).
More recent historians of mathematics have been equally surprised.
Particularly puzzling to Tobias Dantzig was the fact "that the great
mathematicians of Classical Greece did not stumble on it" (ibid., p.
30). For Constance Reid, the great mystery of zero is that "it escaped
even the Greeks" (Reid 1964, p. 4).
Why did the ideas of zero and algebra develop in India and not ancient
Greece? It’s a common question that will be rise in our mind & it is
true.
The answer of this query does not lie in an examination of Greek
mathematics but rather in a comparison of Greek and Hindu
philosophy. Paradoxically, it was the logical thought patterns of the
Greeks that hindered the development of algebra and the invention of
zero.
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16. Conclusion
The Sumerians were the first to develop a counting system to keep an
account of their stock of goods & domestic Animals. The Sumerian
system was positional; that is, the placement of an individual symbol
related to others denoted its value. The Sumerian system was handed
down to the Acadians around 2500 BC.
And then in 2000 BC. It was the Babylonians who first conceived of a
mark to signify that a number was absent from a column; just as 0 in
1025 signifies that there are no hundreds in that number. Although
zero's Babylonian ancestor was a good start, it would still be centuries
before the symbol as we know it appeared.
The popular mathematicians among the Ancient Greeks, who learned
the fundamentals of their math from the Egyptians, did not have a
name for zero, nor did their system feature a placeholder as did the
Babylonian. But actually, there is no exact evidence to say the symbol
even existed in their language. At last, the Indians started to
understand zero both as a symbol and as an idea of number.
Brahmagupta was the first who formalize arithmetic operations using
zero. He used dots to indicate a zero. These dots were alternately
referred to as 'sunya', which means empty. Brahmagupta
experimented by writing standard rules for reaching zero through
addition , subtraction, multiplication as well as the results of
operations with zero. The only error in his rules was division by zero.
But only a few centuries before zero reached Europe. First, the great
Arabian voyagers would bring the texts of Brahmagupta and his
colleagues back from India along with spices and other exotic.
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17. items. by 773 AD Zero reached Baghdad and would be developed in
the Middle East by Arabian mathematicians who would base their
numbers on the Indian system. In the ninth century, Mohammed ibn-
Musa al-Khowarizmi was the first who experimented on equations that
equaled zero, or algebra as it has come to be known. He also
advanced quick methods for multiplying and dividing numbers known
as algorithms (a corruption of his name). Al-Khowarizmi called zero
'sifr', from which our cipher is derived. By 879 AD, zero was written
almost as we now know it, an oval - but in this case smaller than the
other numbers. And salute to the conquest of Spain by the Moors, zero
finally reached Europe; by the middle of the twelfth century,
translations of Al-Khwarizmi’s work had spread throughout England.
Then the Italian mathematician, Fibonacci, built on Al-Khwarizmi’s
work with algorithms in his book Liber Abaci, or "Abacus book," in
1202. Until that time, the abacus had been the most prevalent tool to
perform arithmetic operations. Fibonacci's developments quickly
gained notice by Italian merchants and German bankers, especially
the use of zero. Accountants knew their books were balanced when
the positive and negative amounts of their assets and liabilities
equaled zero.
But governments were still suspicious of Arabic numerals because of
the ease in which it was possible to change one symbol into another.
Though outlawed, merchants continued to use zero in encrypted
messages, thus the derivation of the word cipher, meaning code, from
the Arabic sifr.
The next great mathematician to use zero was Rene Descartes, the
founder of the Cartesian coordinate system.
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18. Although zero was now becoming more common, the fathers of
calculus, Newton and Leibniz, would make the final step in
understanding zero.
Adding, subtracting, and multiplying by zero are relatively simple
operations. But division by zero created confusion even great minds.
How many times does zero go into ten? Or, how many non-existent
apples go into two apples? The answer is indeterminate, but working
with this concept is the key to calculus. For example, when one drives
to the store, the speed of the car is never constant due to stoplights,
traffic jams, and different speed limits all cause the car to speed up or
slow down.Even accident or technical problem of a car can push the
car to stop, But how would one find the exact speed of the car at one
particular instant? This is where zero and calculus enter the picture.
If you wanted to know your speed at a particular instant, you would
have to measure the change in speed that occurs over a set period of
time. By making that set period smaller and smaller, you could
reasonably estimate the speed at that instant.Even you have to know
the time intervals during accident. In effect, as you make the change
in time approach zero, the ratio of the change in speed to the change
in time becomes similar to some number over zero - the same problem
that stumped Brahmagupta.
In the 1600's, Newton and Leibniz solved this problem independently
and opened the world to tremendous possibilities. By working with
numbers as they approach zero, calculus was born without which we
wouldn't have physics, engineering, and many aspects of economics
and finance.
In the twenty-first century zero is so familiar that to talk about it
seems like much ado about nothing. But it is precisely understanding
and working with this nothing that has allowed civilization to progress.
The development of zero across continents, centuries, and minds has
made it one of the greatest accomplishments of human society.
Because math is a global language, and calculus its crowning
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19. achievement, zero exists and is used everywhere.
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20. References
1)Nils-Bertil Wallin. Yale Global, 19 November 2002.
2)Seife, Charles (2000). Zero: The Biography
3)Kaplan, Robert (2000). The Nothing that Is: A Natural History of Zero. New York:Oxford
University Press.
4)Robert K. Logan. Academia, University of Toronto.
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